BA 530 - Financial Management (Charles Hodges) - Chapter 4 Quiz

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An S&L provides a loan with 15 yearly repayments of $8,000 with the first payment beginning immediately. Which of the following amounts comes closest to the present value of the loan if the interest rate is 7%?

$ 77,964 PV = Immediate Pmt + Pmt(PVIFA7%,14) = $8,000 + $8,000(8.7455) = $77,964. In begin mode, pmt=8000, n=15, i=7, fv=0 and solve for pv=77964.

You need a 30-year, fixed-rate mortgage to buy a new home for $240,000. Your mortgage bank will lend you the money at a 7.5 percent APR for this 360-month loan, with interest compounded monthly. However, you can only afford monthly payments of $850, so you offer to pay off any remaining loan balance at the end of the loan in the form of a single balloon payment. What will be the amount of the balloon payment if you are to keep your monthly payments at $850?

$1,115,840 This is fairly simple with a financial calculator. pv=240000, n=360, pmt=-850, i=7.5/12, and compute the fv = 1115839.53. the amount you owe is going up because your payment is not enough to cover the monthly interest, 240000*(7.5%/12)=1500.

What is the future value of a 5-year ordinary annuity with annual payments of $200, evaluated at a 15 percent interest rate?

$1,348.48 Financial calculator solution: Inputs: N = 5; I = 15; PV = 0; PMT = -200. Output: FV = $1,348.48.

What is the future value of a 5-year ordinary annuity with annual payments of $200, evaluated at a 15 percent interest rate?

$1,348.48 Financial calculator solution:Inputs: N = 5; I = 15; PV = 0; PMT = -200. Output: FV = $1,348.48.

You have just taken out an installment loan for $100,000. Assume that the loan will be repaid in 12 equal monthly installments of $9,456 and that the first payment will be due one month from today. How much of your fourth monthly payment will go toward the repayment of interest?

$1,543.70 Given: Loan Value = $100,000; Repayment Period = 12 months; Monthly Payment = $9,456. N = 12PV = -100,000 PMT = 9,456 FV = 0. Solve for I/YR = 2.00% „e 12 = 24.00%. After you get the interest rate, change N=3 and compute future value, $77181.85. Then change N=4 and compute future value, $69269.55. The difference in ending balances is your principal repaid, $7912.30. Then, since Payment = Principal + Interest, solve for interest (9456-7912.30)=1543.70/

What's the future value of $1,200 after 5 years if the appropriate interest rate is 6%, compounded monthly?

$1,618.62 N=5*12=60 I%=6%/12=.5% PV=-1200 PMT=0 FV=1618.62

What's the future value of $1,200 after 5 years if the appropriate interest rate is 6%, compounded monthly?

$1,618.62 N=5*12=60 I=6/12=.5 PV=-1200 PMT=0 FV=1618.62

You deposited $1,000 in a savings account that pays 8 percent interest, compounded quarterly, planning to use it to finish your last year in college. Eighteen months later, you decide to go to the Rocky Mountains to become a ski instructor rather than continue in school, so you close out your account. How much money will you receive?

$1126 Financial calculator solution: Inputs: N = 6; I = 2; PV = -1,000; PMT = 0. Output: FV = $1,126.16

If $100 is placed in an account that earns a nominal 4 percent, compounded quarterly, what will it be worth in 5 years?

$122.02 Financial calculator solution: Inputs: N = 20; I = 1; PV = -100; PMT = 0. Output: FV = $122.02. Use Quarterly compounding

If $100 is placed in an account that earns a nominal 4 percent, compounded quarterly, what will it be worth in 5 years?

$122.02 Financial calculator solution: Inputs: N = 20; I = 1; PV = -100; PMT = 0. Output: FV = $122.02. Use Quarterly compounding

You just deposited $2,500 in a bank account that pays a 4.0% nominal interest rate, compounded quarterly. If you also add another $5,000 to the account one year (4 quarters) from now and another $7,500 to the account two years (8 quarters) from now, how much will be in the account three years (12 quarters) from now?

$16,035.88 This problem involves three separate calculations For the first deposit N=3*4=12 I=4/4=1 PV=-2500 PMT=0 FV=2817.06 For the second deposit N=2*4=8 I=4/4=1 PV=-5000 PMT=0 FV=5414.28 For the third deposit N=1*4=4 I=4/4=1 PV=-7500 PMT=0 FV=7804.53 The last step is to add all the future values =2817.06+5414.28+7804.53 =16035.87

On January 1, 2012, your sister's pet supplies business obtained a 30-year amortized mortgage loan for $250,000 at a nominal annual rate of 7.0%, with 360 end-of-month payments. The firm can deduct the interest paid for tax purposes. What will the interest tax deduction be for 2012?

$17,419.55 First we need to find the PMT N=30*12=360 I=7/12=.5833 PV=250,000 PMT=-1663.256 FV=0 Next, back out and go to a blank screen. In the finance app find ΣInt( ΣInt(Begin Period, End Period) ΣInt(1,12) =17419.55 Or you could do an amortization schedule

A court settlement awarded an accident victim four payments of $50,000 to be paid at the end of each of the next four years. Using a discount rate of 4%, calculate the present value of the annuity.

$181,495 PVannuity = PMT(PVIFA4%,4) = $50,000(3.6299) = $181,495. N=4, pmt=50000, I=4, fv=0 and compute pv=181495.

You want to be a millionaire when you retire in 40 years. You can earn A 12.5 percent annual return. How much more will you have to save each month if you wait 10 years to start saving versus if you start saving at the end of this month?

$183.38 fv=1000000, n=40*12=480, i=12.5/12, pv=0, pmt=72.53. fv=1000000, n=30*12=360, i=12.5/12, pv=0, pmt=255.91. Difference is 183.38.

Jerry and Faith Hudson recently obtained a 30-year (360-month), $250,000 mortgage with a 9 percent nominal interest rate. What will be the remaining balance on the mortgage after five years (60 months)?

$239,700 Step 1 is to find the payment, PV=250000,N=30*12=360,I/Y=9/12=.75,FV=0 and compute PMT=-2011.556542 Step 2, leaving all of the above inputs in you calculator, change n=60 then compute FV=239700.3407. By changing N from 360 to 60 and computing future value, you have computed the amount still owed after 60 payments.

You are considering buying a new car. The sticker price is $15,000 and you have $2,000 to put toward a down payment. If you can negotiate a nominal annual interest rate of 10 percent and you wish to pay for the car over a 5-year period, what are your monthly car payments?

$276.21 First, find the monthly interest rate = 10%/12 = 0.8333% a month. Now, enter in your calculator N = 60, I/YR = 0.8333, PV = -13,000, FV = 0, and solve for PMT = $276.21 monthly payments.

You are planning to save for retirement over the next 15 years. To do this, you will invest $1,100 a month in a stock account and $500 a month in a bond account. The return on the stock account is expected to be 7 percent, and the bond account will pay 4 percent. When you retire, you will combine your money into an account with a 5 percent return. How much can you withdraw each month during retirement assuming a 20-year withdrawal period?

$3,113.04 step 1, find the future value of your deposits. Find fv of stocks, pv=0, pmt=-1100, i=7/12, n=15*12=180, and compute fv=348658.53. Find fv of stocks, pv=0, pmt=-500, i=4/12, n=15*12=180, and compute fv=123045.24. This gives a total of 471703.77. Step 2, use this fv as the new pv in 15 years and solve for payment. pv=471703.77, n=20*12=240, i=5/12, fv=0, and compute the pmt = 3113.04

Given an interest rate of 8 percent per year, what is the value at date t = 9 of a perpetual stream of $500 annual payments that begins at date t = 17?

$3,646.81 This is a sneakily difficult problem. The payments begin at the end of year 17, so the perpetuity value at the end of year 16 =cash flow/rate = 500/.08=6250. We are being asked the value of the perpetuity at the end of year 9. Thus, there are 7 years between 9 and 16. Thus we must solve, fv=6250, n=7, i=8, pmt=0, and solve for pv of 3646.81. Your answer would be unchanged if you assumed the beginning of periods 9 and 17.

Given an interest rate of 8 percent per year, what is the value at date t = 9 of a perpetual stream of $500 annual payments that begins at date t = 17?

$3,646.81 This is a sneakily difficult problem. The payments begin at the end of year 17, so the perpetuity value at the end of year 16 =cash flow/rate = 500/.08=6250. We are being asked the value of the perpetuity at the end of year 9. Thus, there are 7 years between 9 and 16. Thus we must solve, fv=6250, n=7, i=8, pmt=0, and solve for pv of 3646.81. FWIW, the answer key in the testbank was incorrect with 3376.68. This question shows the importance of a timeline. Your answer would be unchanged if you assumed the beginning of periods 9 and 17.

Find the present value of $5,325 to be received in one period if the rate is 6.5%.

$5,000.00 fv=5325, n=1, i=6.5, pmt=0 and compute pv = 5000. Or by math, 5325/1.065

Find the present value of $5,325 to be received in one period if the rate is 6.5%.

$5,000.00 fv=5325, n=1, i=6.5, pmt=0 and compute pv = 5000. Or by math, 5325/1.065.

You have just taken out an installment loan for $100,000. Assume that the loan will be repaid in 12 equal monthly installments of $9,456 and that the first payment will be due one month from today. How much of your third monthly payment will go toward the repayment of principal?

$7,757.16 A problem like this is always on the mid-term and final exams. Given: Loan Value = $100,000; Repayment Period = 12 months; Monthly Payment = $9,456. N = 12; PV = -100,000; PMT = 9,456; FV = 0. Solve for I/YR = 2.00% x 12 months = 24.00%. To find the amount of principal paid in the third month (or period), use the calculator's amortization feature. Enter: 3 INPUT 3 AMORT (to activate the calculator's amortization feature). Interest = $1,698.84. Principal = $7,757.16. Balance = $77,181.86

$7,912.30 Given: Loan Value = $100,000; Repayment Period = 12 months; Monthly Payment = $9,456. N = 12. PV = -100,000. PMT = 9,456. FV = 0. Solve for I/YR = 2.00% which implies a nominal annual rate of 24.00%. After you get the interest rate, change N=3 and compute future value, 77181.85. Then change n=4 and compute future value, 69269.54. The difference in ending balances is your principal repaid, 7912.30.

Your holiday ski vacation was great, but it unfortunately ran a bit over budget. All is not lost. You just received an offer in the mail to transfer your $5,000 balance from your current credit card, which charges an annual rate of 18.7 percent, to a new credit card charging a rate of 9.4 percent. You plan to make payments of $510 a month on this debt. How many less payments will you have to make to pay off this debt if you transfer the balance to the new card?

0.48 payments pv=5000,i=18.7/12,fv=0,pmt=-510, and compute N. pv=5000,i=9.4/12,fv=0,pmt=-510, and compute N. Take the difference in Ns. $5,000 = $510 × [(1 - {1 + (0.094/12)]}t)/(0.094/12)]t = ln (1/0.9232)/ln 1.007833; t = 10.24 payments Difference = 10.72 - 10.24 = 0.48 payments

You are planning on taking a loan for $ 17 ,000. You will repay the loan in annual payments over the next 16 years and the loan has a stated interest rate of 2 %. For the very last payment on your loan, how much of this is repayment of principal? For example, if the loan payment is $400 of which $30 is interest and $370 is principal, your answer is $370. Enter your answer to the nearest $.01. Do not use $ or , signs in your answer. Enter your answer as a positive number.

1,227.50 This is an ordinary annuity, so set your calculator to END mode. Input N, I, PV and FV = 0 to solve for PMT. Next, without clearing the calculator, change N to Number of Years minus 1 year (e.g. for a 10 year loan, enter 9), then compute Future Value. This Future Value is the beginning balance in the last year and is therefore your principal. Note, Excel gives an incorrect answer if you use a spreadsheet to solve.

You have just taken out a 17 -year, $ 182 ,000 mortgage loan at an annual interest rate of 7.8 percent. The mortgage has monthly payments. What is the amount of each payment? Calculate your answer to the nearest $.01. Enter your answer as a positive number. Do not use the $ or , sign.

1,613.21 In the financial calculator, input N=number of years*number of payments made in a year; I%=interest rate/number of payments made in a year; make sure calculator is in END mode. Solve for PMT

Assume that you have a lump sum $ 862 that you are investing for 3 years at a nominal rate of 24 %. What is the expected Future Value? Enter your answer to the nearest $.01. Do not use $ or , signs in your answer. Enter your answer as a positive number.

1,643.51 Future Value = Present Value (PV) * (1 + Nominal Rate) to the Number of Years (N) Power. In the calculator, enter PV, N, and I (I/Y) then calculate FV.

Partners Bank offers to lend you $50,000 at a nominal rate of 5.0%, simple interest, with interest paid quarterly. An offer to lend you the $50,000 also comes from Community Bank, but it will charge 6.0%, simple interest, with interest paid at the end of the year. What's the difference in the effective annual rates charged by the two banks?

1.56% Simple Interest=Interest earned only on the principle EFF=(1+periodic interest rate)^M times per year-1.0 Partners =((1+.0125)^4)-1 =5.09% Community =((1+.06)^1)-1 =6% Then simply find the difference 6%-5.09%=.91%

Your credit card, upon which you make monthly payments, has a quoted annual interest rate of 21.8 . What is the periodic interest rate? Calculate your answer to the nearest .01%. Do not use the % sign in your answer. Thus .83% would be .83 rather than .83% or .0083.

1.82 Periodic Rate = Nominal Rate/12

What is the future value of a 5-year annuity due with annual payments of $ 1,413 , evaluated at a 14.68 percent interest rate? Enter your answer to the nearest $.01. Do not use $ or , signs in your answer. Enter your answer as a positive number.

10,856.52 Set your calculator to begin mode, then N=5, I = the interest rate, PMT= payment, PV=0, then compute FV.

You are preparing to make monthly payments of $72, beginning at the end of this month, into an account that pays 6 percent interest compounded monthly. How many payments will you have made when your account balance reaches $9,312?

100 pv=0, pmt=-72, fv=9312, i=6/12=.5 and compute N= 99.9997

Your uncle has $300,000 invested at 7.5%, and he now wants to retire. He wants to withdraw $35,000 at the end of each year, beginning at the end of this year. He also wants to have $25,000 left to give you when he ceases to withdraw funds from the account. What is the maximum number of $35,000 withdrawals that he can make and still have at least $25,000 left in the account? (Hint: If your solution for N is not an integer, round down to the nearest whole number.)

12 I/YR = 7.50% PV = -$300,000 PMT = $35,000 FV = $25,000 N = 13.48 N rounded = 13

You are planning on taking a loan for $ 86 ,000. You will repay the loan in annual payments over the next 8 years and the loan has a stated interest rate of 12 %. For the very last payment on your loan, how much of this is repayment of principal? For example, if the loan payment is $400 of which $30 is interest and $370 is principal, your answer is $370. Enter your answer to the nearest $.01. Do not use $ or , signs in your answer. Enter your answer as a positive number.

15,457.18 This is an ordinary annuity, so set your calculator to END mode. Input N, I, PV and FV = 0 to solve for PMT. Next, without clearing the calculator, change N to Number of Years minus 1 year (e.g. for a 10 year loan, enter 9), then compute Future Value. This Future Value is the beginning balance in the last year and is therefore your principal. Note, Excel gives an incorrect answer if you use a spreadsheet to solve.

What is the future value of a 7-year annuity due with annual payments of $ 1,827 , evaluated at a 7.64 percent interest rate? Enter your answer to the nearest $.01. Do not use $ or , signs in your answer. Enter your answer as a positive number.

17,355.16 Set your calculator to begin mode, then N=7, I = the interest rate, PMT= payment, PV=0, then compute FV.

What is the future value of a 5-year ordinary annuity with annual payments of $ 2,799 , evaluated at a 17.08 percent interest rate? Enter your answer to the nearest $.01. Do not use $ or , signs in your answer. Enter your answer as a positive number.

19,664.35 Use the equation FVn=PV (1+I)^n or, set your calculator to end mode, then N=5, I = the interest rate, PMT= payment, PV=0, then compute FV.

What is the future value of a 7-year annuity due with annual payments of $ 1,658 , evaluated at a 15.19 percent interest rate? Enter your answer to the nearest $.01. Do not use $ or , signs in your answer. Enter your answer as a positive number.

21,260.27 Set your calculator to begin mode, then N=7, I = the interest rate, PMT= payment, PV=0, then compute FV.

Assume that you have a lump sum $ 224 that you are investing for 4 years at a nominal rate of 7 %. What is the expected Future Value? Enter your answer to the nearest $.01. Do not use $ or , signs in your answer. Enter your answer as a positive number.

293.62 Future Value = Present Value (PV) * (1 + Nominal Rate(I/Y)) to the Number of Years (N) Power.With PV, N, I/Y then calculate FV.

Pacific Bank pays a 4.50% nominal rate on deposits, with monthly compounding. What effective annual rate (EFF%) does the bank pay?

4.59% Eff=((1+periodic rate)^m) -1 =((1+.00375)^12)-1 =.0459 OR TI-84 Apps>Finance>Eff( Eff(Interest rate,Periods per year) =Eff(4.5,12) =4.59

You want to make an investment that will yield a lump sum of $ 70,952 in 5 years. You will invest at a nominal rate of 12 %. How much do you need to invest today to reach the above future value? Enter your answer to the nearest $.01. Do not use $ or , signs in your answer. Enter your answer as a positive number.

40,260.07 Present Value (PV) = Future Value (FV)/((1 + Nominal Rate(I/Y)) to the Number of Years (N) Power).With FV, N, I/Y then calculate PV.

You have just purchased a new warehouse. To finance the purchase, you've arranged for a 30-year mortgage loan for 80 percent of the $2,600,000 purchase price. The monthly payment on this loan will be $12,200. What is the effective annual rate on this loan?

5.95% This tests your knowledge of the various interest rates. pv=Loan amount = $2,600,000 × 0.80 = $2,080,000, n=30*12=360, pmt=-12200, fv=0, and compute I=.483%. Multiply this by 12 to get the nominal rate of 5.79%. Now convert the nominal to the effective with 12 payments per year of 5.95%.

What is the future value of a 5-year ordinary annuity with annual payments of $ 1,219 , evaluated at a 17.65 percent interest rate? Enter your answer to the nearest $.01. Do not use $ or , signs in your answer. Enter your answer as a positive number.

8,660.98 Use the equation FVn=PV (1+I)^n or, set your calculator to end mode, then N=5, I = the interest rate, PMT= payment, PV=0, then compute FV.

You want to borrow $47,170 from your local bank to buy a new sailboat. You can afford to make monthly payments of $1,160, but no more. Assume monthly compounding. What is the highest rate you can afford on a 48-month APR loan?

8.38 percent

You have just taken out an installment loan for $100,000. Assume that the loan will be repaid in 12 equal monthly installments of $9,456 and that the first payment will be due one month from today. How much of your third monthly payment will go toward the repayment of principal? A. $7,757.16 B. $6,359.12 C. $7,212.50 D. $7,925.88 E. $8,333.33

A. $7,757.16 (MId-Term & Final) Given: Loan Value = $100,000; Repayment Period = 12 months; Monthly Payment = $9,456. N = 12; PV = -100,000; PMT = 9,456; FV = 0. Solve for I/YR = 2.00% x 12 months = 24.00%. To find the amount of principal paid in the third month (or period), use the calculator's amortization feature. Enter: 3 INPUT 3 AMORT (to activate the calculator's amortization feature). Interest = $1,698.84. Principal = $7,757.16. Balance = $77,181.86. Given: Loan Value = $100,000; Repayment Period = 12 months; Monthly Payment = $9,456.N = 12PV = -100,000PMT = 9,456FV = 0Solve for I/YR = 2.00% x 12 = 24.00%. To find the amount of principal paid in the third month (or period), use the calculator's amortization feature. Enter: 3 INPUT 3 AMORT (to activate the calculator's amortization feature). Interest = $1,698.84Principal = $7,757.16Balance = $77,181.86

Your bank account pays a 5% nominal rate of interest. The interest is compounded quarterly. Which of the following statements is CORRECT? A. The periodic rate of interest is 1.25% and the effective rate of interest is greater than 5%. B. The periodic rate of interest is 5% and the effective rate of interest is greater than 5%. C. The periodic rate of interest is 1.25% and the effective rate of interest is 2.5%. D. The periodic rate of interest is 5% and the effective rate of interest is also 5%.

A. The periodic rate of interest is 1.25% and the effective rate of interest is greater than 5%. periodic rate=Nominal/number of compounding periods per year = 5%/4 = 1.25%

You are considering two equally risky annuities, each of which pays $15,000 per year for 20 years. Investment ORD is an ordinary (or deferred) annuity, while Investment DUE is an annuity due. Which of the following statements is CORRECT? A. The present value of DUE exceeds the present value of ORD, and the future value of DUE also exceeds the future value of ORD. B. The present value of ORD exceeds the present value of DUE, and the future value of ORD also exceeds the future value of DUE. C. The present value of DUE exceeds the present value of ORD, while the future value of DUE is less than the future value of ORD. D. The present value of ORD must exceed the present value of DUE, but the future value of ORD may be less than the future value of DUE.

A. The present value of DUE exceeds the present value of ORD, and the future value of DUE also exceeds the future value of ORD. Annuities due have greater future values because the payments will earn interest for one additional period. Annuities due have greater present value because the payments are discounted for one less period.

The greater the number of compounding periods within a year, then (1) the greater the future value of a lump sum investment at Time 0 and (2) the smaller the present value of a given lump sum to be received at some future date. A. True B. False

A. True Future value=PV(1+I)^N Present Value=FV/(1+I)^N Plug in numbers if you are having a hard time with this problem conceptually.

The payment made each period on an amortized loan is constant, and it consists of some interest and some principal. The closer we are to the end of the loan's life, the greater the percentage of the payment that will be a repayment of principal. A. True B. False

A. True intitally more interest is paid per payment than the principle. Over time this reverses.

Compound interest A. allows for the reinvestment of interest payments. B. does not allow for the reinvestment of interest payments. C. is the same as simple interest. D. provides a value that is less than simple interest. E. Both A and D.

A. allows for the reinvestment of interest payments. See Page 44

Present value may be defined as A. future cash flows discounted to the present. B. estimated future cash flow in year n + 1. C. present cash flows compounded into the future. D. the average of the bid and asked price. E. None of the above.

A. future cash flows discounted to the present. See Page 46

In future value problems, the discount rate is adjusted A. upward to reflect higher risk and to increase the future cash flows. B. upward to reflect higher risk and to reduce the future cash flows. C. downward to reflect higher risk and to increase the future cash flows. D. downward to reflect higher risk and to reduce the future cash flows. E. None of the above.

A. upward to reflect higher risk and to increase the future cash flows. To compensate for higher risk, one must get a higher return. This can be reflected three ways, a higher payment, a higher future value, or a lower present value. Therefore, "upward to reflect higher risk and to increase the future cash flows."

B. $1,115,840 This is fairly simple with a financial calculator. pv=240000, n=360, pmt=-850, i=7.5/12, and compute the fv = 1115839.53. the amount you owe is going up because your payment is not enough to cover the monthly interest, 240000*(7.5%/12)=1500.

Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years. By how much would you reduce the amount you owe in the first year? A. $2,404.91 B. $2,531.49 C. $2,658.06 D. $2,790.96

B. $2,531.49 First we need to find the amount of each payment N=5 I=8.5 PV=-15,000 PMT=3,806.49 FV=0 Next we need to find the first years interest payment. =15,000*.085 =1,275 Now to find how much was paid towards the principle, remember interest is paid first. 3806.49-1275=2531.49 OR you can use the TI-84 calculator function After entering the correct TVM solver inputs to find the PMT. Under the finance application scrow down and find the function ΣInt( ΣInt(Begin Period, End Period) The beginning period is 1 and also the end period is 1. If we wanted total interest paid on the duration of the loan the end period would be 4 but since we need interest on a single payment the begin period is the same as the end. ΣInt(1, 1) =2531.49

B. 5.95% This tests your knowledge of the various interest rates. pv=Loan amount = $2,600,000 × 0.80 = $2,080,000, n=30*12=360, pmt=-12200, fv=0, and compute I=.483%. Multiply this by 12 to get the nominal rate of 5.79%. Now convert the nominal to the effective with 12 payments per year of 5.95%.

The present value of a future sum increases as either the discount rate or the number of periods per year increases, other things held constant. A. True B. False

B. False Present value= Future Value/((1+interest rate)^Number of compounding periods) Increasing the dominator of a fraction decreases the end number.

Suppose Randy Jones plans to invest $1,000. He can earn an effective annual rate of 5% on Security A, while Security B has an effective annual rate of 12%. After 11 years, the compounded value of Security B should be somewhat less than twice the compounded value of Security A. (Ignore risk, and assume that compounding occurs annually.) A. True B. False

B. False Work out the numbers with a calculator: PV = 1000 FVA = $1,710.34 Rate on A = 5% 2 x FVA = $3,420.68 Rate on B = 12% FVB = $3,478.55 Years = 11 FVB > 2 ´ FVA, so = FALSE

An ordinary annuity is best defined by which one of the following? A. increasing payments paid forever B. equal payments paid at regular intervals over a stated time period C. equal payments paid at regular intervals of time on an ongoing basis D. unequal payments that occur at set intervals for a limited period of time E. increasing payments paid for a definitive period of time

B. equal payments paid at regular intervals over a stated time period See the definition. Also, this is end of period cash flows.

You are hoping to buy a new boat 3 years from now, and you plan to save $4,200 per year, beginning one year from today. You will deposit your savings in an account that pays 5.2% interest. How much will you have just after you make the 3rd deposit, 3 years from now? A. $11,973 B. $12,603 C. $13,267 D. $13,930

C. $13,267 N = 3 I/YR = 5.2% PV = $0.00 PMT = $4,200 FV = $13,266.56

C. $276.21 First, find the monthly interest rate = 10%/12 = 0.8333% a month. Now, enter in your calculator N = 60, I/YR = 0.8333, PV = -13,000, FV = 0, and solve for PMT = $276.21 monthly payments.

Which of the following statements regarding a 20-year (240-month) $225,000, fixed-rate mortgage is CORRECT? (Ignore taxes and transactions costs.) A. The outstanding balance declines at a slower rate in the later years of the loan's life. B. The remaining balance after three years will be $225,000 less one third of the interest paid during the first three years. C. Because it is a fixed-rate mortgage, the monthly loan payments (which include both interest and principal payments) are constant. D. Interest payments on the mortgage will increase steadily over time, but the total amount of each payment will remain constant.

C. Because it is a fixed-rate mortgage, the monthly loan payments (which include both interest and principal payments) are constant.

You are investing $100 today in a savings account at your local bank. Which one of the following terms refers to the value of this investment one year from now? A. cash flows B. Present value C. Future Value D. time period E. Invested Principal

C. Future Value It is a value in the future, future value.

You plan to analyze the value of a potential investment by calculating the sum of the present values of its expected cash flows. Which of the following would increase the calculated value of the investment? A. The discount rate increases. B. The cash flows are in the form of a deferred annuity, and they total to $100,000. You learn that the annuity lasts for 10 years rather than 5 years, hence that each payment is for $10,000 rather than for $20,000. C. The discount rate decreases. D. The riskiness of the investment's cash flows increases.

C. The discount rate decreases. Decreasing the discount rate would cause the present value to increase because it would affect the dominator in the fraction used to discount and find present value.

You plan to analyze the value of a potential investment by calculating the sum of the present values of its expected cash flows. Which of the following would lower the calculated value of the investment? A. The discount rate decreases. B. The cash flows are in the form of a deferred annuity, and they total to $100,000. You learn that the annuity lasts for only 5 rather than 10 years, hence that each payment is for $20,000 rather than for $10,000. C. The discount rate increases. D. The riskiness of the investment's cash flows decreases.

C. The discount rate increases. Increasing the discount rate would raise the dominator of the fraction used to find present value and thus would lower it.

An annuity A. is a debt instrument that pays no interest. B. is a stream of payments that varies with current market interest. C. is a level stream of equal payments through time. D. has no value. E. None of the above.

C. is a level stream of equal payments through time. See Page 50-51

If the compound period is greater than one A. the effective annual interest rate is always equal to the annual percentage rate. B. the effective annual interest rate is always less than the annual percentage rate. C. the effective annual interest rate is always greater than the annual percentage rate. D. the effective annual interest rate is never greater than the annual percentage rate. E. None of the above.

C. the effective annual interest rate is always greater than the annual percentage rate. See Page 64

What is the present value of $1,100 per year, at a discount rate of 10 percent if the first payment is received 6 years from now and the last payment is received 30 years from now? A. $6,333.33 B. $6,511.08 C. $6,420.12 D. $6,238.87 D. $6,199.74

D. $6,199.74 This is easy with a financial calculator. Assume payments are made at the end of the year. Cash flows 0, 1-5 are 0 cash flows 6 to 30 are 1100, with an interest rate of 10%. Cash flow 0 is 0, Cash flow 1 is 0 with frequency of 5. Cash flow 2 is 1100 with frequency of 25. NPV@10% is 6199.74

How much would Roderick have after 6 years if he has $500 now and leaves it invested at 5.5% with annual compounding? A. $591.09 B. $622.20 C. $654.95 D. $689.42

D. $689.42 N = 6 I/YR = 5.5% PV = $500 PMT = $0 FV = $689.42

Which of the following bank accounts has the lowest effective annual return? A. An account that pays 8% nominal interest with daily (365-day) compounding. B. An account that pays 8% nominal interest with monthly compounding. C. An account that pays 7% nominal interest with daily (365-day) compounding. D. An account that pays 7% nominal interest with monthly compounding.

D. An account that pays 7% nominal interest with monthly compounding. The number of compounding periods will increase the effective rate.

You plan to invest some money in a bank account. Which of the following banks provides you with the highest effective rate of interest? A. Bank 1; 6.1% with annual compounding. B. Bank 2; 6.0% with monthly compounding. C. Bank 4; 6.0% with quarterly compounding. D. Bank 5; 6.0% with daily (365-day) compounding.

D. Bank 5; 6.0% with daily (365-day) compounding. See effective rate of interest forumula in book.

The future value of a lump sum at the end of five years is $1,000. The nominal interest rate is 10 percent and interest is compounded semiannually. Which of the following statements is most correct? A. The present value of the $1,000 is greater if interest is compounded monthly rather than semiannually. B. The effective annual rate is greater than 10 percent. C. The periodic interest rate is 5 percent. D. Both statements b and c are correct. E. All of the statements above are correct.

D. Both statements b and c are correct. This question tests several time value concepts. With more than one compounding period per year, the effective rate is greater than the nominal rate which is greater than the periodic rate. For a given nominal rate, increasing the number of compounding periods per year will increase the annual effective rate. The highest effective rate is associated with continuous compounding. The periodic rate is calculated as the nominal rate divided by the number of periods per year. wrong

Of the following investments, which would have the lowest present value? Assume that the effective annual rate for all investments is the same and is greater than zero. A. Investment A pays $250 at the end of every year for the next 10 years (a total of 10 payments). B Investment B pays $125 at the end of every 6-month period for the next 10 years (a total of 20 payments). C. Investment C pays $125 at the beginning of every 6-month period for the next 10 years (a total of 20 payments). D. Investment D pays $2,500 at the end of 10 years (just one payment).

D. Investment D pays $2,500 at the end of 10 years (just one payment). PV=FV/(1+I)^N

Which of the following statements is most correct? A. The first payment under a 3-year, annual payment, amortized loan for $1,000 will include a smaller percentage (or fraction) of interest if the interest rate is 5 percent than if it is 10 percent. B. If you are lending money, then, based on effective interest rates, you should prefer to lend at a 10 percent nominal, or quoted, rate but with semiannual payments, rather than at a 10.1 percent nominal rate with annual payments. However, as a borrower you should prefer the annual payment loan. C. The value of a perpetuity (say for $100 per year) will approach infinity as the interest rate used to evaluate the perpetuity approaches zero. D. Statements a, b, and c are all true. E. Statements b and c are true.

D. Statements a, b, and c are all true. See Page 64, 69-70 First Three Answers Are Correct

A $250,000 loan is to be amortized over 8 years, with annual end-of-year payments. Which of these statements is CORRECT? A. The proportion of interest versus principal repayment would be the same for each of the 8 payments. B. The annual payments would be larger if the interest rate were lower. C. If the loan were amortized over 10 years rather than 8 years, and if the interest rate were the same in either case, the first payment would include more dollars of interest under the 8-year amortization plan. D. The proportion of each payment that represents interest as opposed to repayment of principal would be lower if the interest rate were lower.

D. The proportion of each payment that represents interest as opposed to repayment of principal would be lower if the interest rate were lower. Interest will always be paid first in ammortization so having a lower interest rate would free up more of each payment to pay towards the principle.

Which of the following statements is CORRECT? A. Some of the cash flows shown on a time line can be in the form of annuity payments, but none can be uneven amounts. B. A time line is not meaningful unless all cash flows occur annually. C. Time lines are not useful for visualizing complex problems prior to doing actual calculations. D. Time lines can be constructed for annuities where the payments occur at either the beginning or the end of the periods.

D. Time lines can be constructed for annuities where the payments occur at either the beginning or the end of the periods. Time lines can be constructed for annuities due and deferred annuities

Interest earned on both the initial principal and the interest reinvested from prior periods is called: interest on interest. A. dual interest. B. free interest. C. simple interest. D. compound interest.

D. compound interest. interest on interest is compound interest.

The stated rate of interest is 10%. Which form of compounding will give the highest effective rate of interest? A. annual compounding B. monthly compounding C. daily compounding D. continuous compounding E. It is impossible to tell without knowing the term of the loan.

D. continuous compounding incorrect, the more frequent the compounding, the higher the effective rate.

Which of the following statements is most correct? A. A 5-year $100 annuity due will have a higher present value than a 5- year $100 ordinary annuity. B. A 15-year mortgage will have larger monthly payments than a 30-year mortgage of the same amount and same interest rate. C. If an investment pays 10 percent interest compounded annually, its effective rate will also be 10 percent. D. Statements a and c are correct. E. All of the statements above are correct.

E. All of the statements above are correct. see page 74-77, 85-86, 88-90

The interest rate that is quoted by a lender is referred to as which one of the following? A. simple rate B. effective annual rate C. wrong answer rate D. common rate E. stated interest rate, also known as the nominal rate, quoted rate, annual percentage rate, discount rate, compound rate, interest rate, yield to maturity, required return, and many other names. All of these are annual nominal rates, that do not consider inter-year compounding of interest.

E. stated interest rate, also known as the nominal rate, quoted rate, annual percentage rate, discount rate, compound rate, interest rate, yield to maturity, required return, and many other names. All of these are annual nominal rates, that do not consider inter-year compounding of interest. stated interest rate, also known as the quoted rate, annual percentage rate, discount rate, compound rate, interest rate, yield to maturity, required return, and many other names.

If we are given a periodic interest rate, say a monthly rate, we can find the nominal annual rate by dividing the periodic rate by the number of periods per year. A. True B. False

F. False Periodic rate=Nominal/number of compounding periods To find the nominal annual rate, you would have to multiply the monthly rate by the number of compounding periods.

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