Finance exam

1. Andy deposited $3,000 this morning into an account that pays 5 percent interest, compounded annually. Barb also deposited $3,000 this morning into an account that pays 5 percent interest, compounded annually. Andy will withdraw his interest earnings and spend it as soon as possible. Barb will reinvest her interest earnings into her account. Given this, which one of the following statements is true?

A. Barb will earn more interest the second year than Andy.

1. Luis is going to receive $20,000 six years from now. Soo Lee is going to receive $20,000 nine years from now. Which one of the following statements is correct if both Luis and Soo Lee apply a 7 percent discount rate to these amounts?

A. In today's dollars, Luis's money is worth more than Soo Lee's.

1. Samantha opened a savings account this morning. Her money will earn 3.5 percent interest, compounded annually. After four years, her savings account will be worth $5,000. Assume she will not make any withdrawals. Given this, which one of the following statements is true?

A. Samantha could have deposited less money today and still had $5,000 in four years if she could have earned a higher rate of interest.

1. Renee invested $2,000 six years ago at 4.5 percent interest. She spends her earnings as soon as she earns any interest so she only receives interest on her initial $2,000 investment. Which type of interest is she earning?

A. Simple interest.

You are planning to save for retirement over the next 45 years. To do this, you will invest $450 a month in a stock account and $300 a month in a bond account, beginning one month from today. The return on the stock account is expected to be 9.0 percent, and the bond account will pay 5.2 percent. When you retire, you will combine your money into an account with a 5.6 percent return. You plan to make equal monthly withdrawals for 30 years from your retirement account beginning one month from your date of retirement. You also plan to leave $6 million as bequest to your beneficiaries. Calculate the amount of your monthly withdrawals.

Amount in Stock Fund at retirement: N = 540 (45x12); I/Y = 9.0/12 = 0.75; PV = 0; PMT = -450; CPT FV. FV = 3,332,195.31 Amount in Bond Fund at retirement: N = 540; I/Y = 5.2/12 = 0.43333333; PV = 0; PMT = -300; CPT FV. FV = 645,846.07 Total Amount in retirement account = 3,332,195.31 + 645,846.07 = $3,978,041.38 Now, in retirement, we have the following: N = 360; PV = - 3,978,041.38; I/Y = 5.6/12 = 0.46666667; FV = 6,000,000; CPT PMT. PMT = $16,392.36 per month.

1. This morning, you opened an account and deposited $1000 into it. The account pays interest of 8 percent per year, compounded annually. If you do not make any additional deposits into the account or withdraw from the account, how much will be in the account 13 years from today?

Answer. FV = 1000(1.08)13 = $2,719.62 Using your calculator's keys: N = 13; PV = - 1000; PMT = 0; I/Y = 8; CPT FV

1. You borrowed $15,000 from a credit card company this morning. The stated interest rate is 9 percent per year compounded monthly. You will not make any payment until 10 years from today when you will be required to make all the payment due as one bulk amount. How much will you have to pay the credit card company 10 years from today?

Answer. Since interest is compounded more than once a year, we need to compute the effective annual rate. This is the rate that will be used as I/Y. Effective annual rate is (1 + 0.09/12)12 - 1 = 9.3807% Thus, FV = 15000(1.093807)10 = $36,770 N = 10; PV = - 15000; I/Y = 9.38; PMT = 0; CPT FV FV = $36,768.

Professor Chuck Tiger is 55 years old. He has decided to invest a certain amount of money in a trust fund each year, beginning one year from today, until he turns 85. Beginning one year after this time, he wants his descendants to be able to withdraw $1 million a year from the trust fund forever. Assume the rate of return for the trust fund is 6 percent in perpetuity. How much should Professor Tiger invest each year in the next thirty years?

Answer. The amount of money he needs in the trust fund at the time he turns 85 is the present value of a perpetuity of $1 million a year. This is equal to 1000000/0.06 = $16,666,666.67 This amount should be the future value of an annuity of a certain amount for thirty years, given interest rate of 6 percent. N = 30; I/Y = 6; PV = 0; FV = -16,666,666.67 CPT PMT. PMT = $210,815.19

In question 11 above, you reckon that Professor Tiger doesn't have time on his side. You just turned 25 and decide to invest a certain amount each year in a Trust Fund until you turn 65. You plan to let your descendants withdraw $200,000 each year from the Trust Fund, beginning a year after you turn 24. Your investments will yield 9 percent per year until you turn 65. Thereafter, the interest rate will be 6 percent per year in perpetuity. How much do you have to invest each year for the next forty years?

Answer: As before, you first have to determine the value of the perpetuity at the time you turn 65. This is equal to 200000/0.06 = $3,333,333.33. This is the amount you should have in the Trust Fund at the time you turn 65. Therefore, we have the following: N = 40; I/Y = 9; PV = 0; FV = - 3,333,333.33; CPT PMT. PMT = $9,865.34

1. What is the effective annual interest rate for a stated interest rate of 11 percent compounded daily?

Answer: Effective annual rate = (1 + 0.11/365)365 - 1 = 11.63% If you wish to use your financial keys to get your answer, you can set up your work as follows: N = 365; I/Y = 11/365 = 0.030136986 (just input whatever comes out as the answer without rounding); PV = -1; PMT = 0; CPT FV FV = 1.11626.

1. What is the present value of an annuity of $12,000 per year for 10 years beginning one year from today, if the discount rate is 7 percent per year?

Answer: PMT = - 12000; I/Y = 7; N = 10; FV = 0; CPT PV. PV = $84,282.98

1. What is the future value of an annuity of $12,000 per year for 10 years beginning one year from today, if the interest rate is 7 percent per year?

Answer: PMT = - 12000; I/Y = 7; N = 10; PV = 0; CPT FV. FV = $165,797.38 or 84,282.98(1.07)10 = $165,797.38

In question 10 above, assume Professor Chuck Tiger can actually get a rate of return of 9 percent on his investment until he turns 85. Thereafter, he will invest more conservatively in an investment that yields 6 percent per year in perpetuity. Now, how much does he need to invest each year for the next thirty years?

Answer: Still he needs to have $16,666,666.67 in the Trust Fund at age 85. However, the I/Y for the thirty investment period changes to 9. N = 30; I/Y = 6; PV = 0; FV = -16,666,666.67; CPT PMT. PMT = $122,272.52

1. What is the present value of an annuity due of $12,000 for 10 years (first payment occurs today) if the discount rate is 7 percent per year?

Answer: The present value of an annuity due is equal to the present value of a regular annuity multiplied by (1+r). In this case, it is given by 84,282.98(1.07) = $90,182.79

1. Your child turned one today. You have decided to invest some money to pay for the child's college education. Assuming you have found an investment instrument that has a rate of return of 7 percent per year, how much will do you need to invest today so that your child's education account will have $70,000 by the time she turns eighteen?

Answer: You have been asked to find the present value of a future amount sitting 17 years from today. N = 17; I/Y = 7; PMT = 0; FV = - 70000; CPT PV. PV = $22,160

You are looking for a loan of $10,000. Four banks have offered you the following loan terms. You have decided to accept one of these loans. Which loan should you accept? Bank A: Interest rate of 18.9 percent compounded annually Bank B: Interest rate of 18.3 percent compounded semiannually Bank C: Interest rate of 17.5 percent compounded monthly Bank D: Interest rate of 17.0 percent compounded daily

Calculate the effective annual interest rate for each bank and select the bank with the lowest effective annual interest rate. Effective Annual Interest Rate for: Bank A: 18.9% Bank B: (1+0.083/2)2 - 1 = 19.14% Bank C: (1+0.175/12)12 - 1 = 18.97% Bank D: (1+0.17/365)365 - 1 = 18.5% Select Bank D. It has the lowest effective annual interest rate on your loan.

You are considering borrowing money from a bank. You have received the following quotations from four banks. Which bank should you borrow from? Bank A: APR of 4.78 percent compounded annually Bank B: APR of 4.73 compounded semi-annually Bank C: APR of 4.70 compounded monthly Bank D: APR of 4.71 percent compounded daily

Calculate the effective annual rates and select the bank with the lowest effective annual rate. Bank A. Effective annual rate = 4.78 percent Bank B. Reffective = (1 + 0.0473/2)2- 1 = 4.786 percent Bank C: Reffective = (1 + 0.0470/12)12- 1 = 4.803 percent Bank D: Reffective = (1 + 0.0471/365)365- 1 = 4.822 percent. Bank A has the lowest effective annual rate.

You are buying your first home using a 30-year mortgage. The mortgage rate is 3.25 percent and the purchase price of the home is $126,000. Your down-payment is 10 percent of the purchase price. Calculate your monthly mortgage payment (of principal and interest).

Down payment = 0.1*126000 = $12,600 Amount borrowed = 126,000 - 12,600 = $113,400 N = 360; I/Y = 3.25/12 = 0.270833333; PV = -113,400; FV = 0; CPT PMT. PMT = 493.52

1. You would like to give your daughter $75,000 towards her college education 17 years from now. How much money must you set aside today for this purpose if you can earn 8 percent on your investments? A. $18,388.19 B. $20,270.17 C. $28,417.67 D. $29,311.13 E. $32,488.37

FV = - $75000; N = 17; I/Y = 8; PMT =0: CPT PV; PV = $20,270.17 Present value = $75,000/(1 + .08)17 = $20,270.17

Your grandmother just gave you $17,000 as a gift for your stellar academic performance. You immediately invested the amount in an account that pays an interest rate of 5.8 percent per year. How much will you have in your account 9 years from today?

FV = 17000(1.058)9 = 28,237.09

Find the future value of $85,000 invested for 14 years at an interest rate of 7.4 percent per year compounded monthly.

FV = 85000x(1 + 0.074/12)12x14 = $238,762.6578 Alternatively, first find the effective annual rate. reff = (1 + 0.074/12)12 - 1 = 7.6562147% Then FV = 85000x(1.076562147)14 = $238,762.6578 Using the Financial Calculator is also an option N = 168 (12 x 14); PV = -85000; PMT = 0; I/Y = 0.616666667 (7.4/12); CPT FV. FV = $238,762.6578

formulas for exam

FV=PV(1+r)^t PV=FV/(1+r)^t PVperpetuity=C/r EAR = (1+APR/m)^m - 1 EAR =e^APR -1 Continuous compounding Annuities: PV = C{(1-1/1+r^t)/r} FV = C{((1+r^t)-1)/r} PVannuity due = PVordinary annuity x (1 + r) FVannuity due = FVordinary annuity x (1 + r) PMTannuity due = PMTordinary annuity/(1 + r)

You are given that the present value (value at time t = 0) of the following cash flow stream is $15,750. The appropriate discount rate is 7.4 percent. What is the missing cash flow? YearCash Flow $4,200 $4,200 ???? $3,700 $3,700

Find the NPV of the cash flow assuming initially that the cash flow at time t = 3 is zero. CF0 = 0; C01 = 4200; F01 = 2; C02 = 0; F02 = 1; C03 = 3700; F02 = 2; NPV. I = 7.4; CPT. NPV = $12,921.97. This implies that the present value of the cash flow at t = 3 is equal to 15750 - 12921.97 = 2,828.03. Find the amount at t=3 whose present value is equal to 2828.03. That is, find the future value of this amount at t=3. FV = 2828.03*(1.074)3 = 3,503.46

You borrowed $370,000 to purchase a home using a fifteen year mortgage with a stated rate of 2.75 percent per year, and monthly payment. Calculate your loan balance just after making payments for ten years.

First find the monthly payment: N = 180 (12x15); PV = -370,000; I/Y = 2.75/12 = 0.229166667; FV = 0; CPT PMT. PMT = $2,510.90. After making payments for ten years (that is, 120 monthly payments made), the loan balance is the "present value" of the remaining 60 monthly payments of 2,510.90 N = 60; PMT = - 2,510.90; I/Y = 0.229166667; FV = 0; CPT PV. PV = $140,605.1476 Alternatively, the loan balance is obtained by finding the FV, the lump sum amount at time t = 120. N = 120; PV = - 370,000; PMT = - 2,510.90; I/Y = 0.229166667; CPT FV. FV = $140,605.1476

You just purchased a brand new BMW 7-series for $87,600 using a dealer loan at an interest rate of 5.92 percent and zero down payment. The terms of the loan call for equal annual payments for seven years, with the first payment made one year from today. Calculate your loan balance just after making your third payment.

First, determine the annual payment amount. N = 7; I/Y = 5.92; PV = -87,600; FV = 0; CPT PMT. PMT = $15,647.64 After making the third payment, the loan balance is the present value of the four remaining payments: N = 4; I/Y = 5.92; PMT = -15,647.64; FV = 0; CPT PV. PV = 54,320.19

You borrow $365,000 to buy a house. The mortgage rate is 2.85 percent. The loan is to be repaid in equal monthly payments over 15 years. All taxes and insurance premiums are to be paid separately. How much of the 34th (monthly) payment applies to the principal balance?

First, determine the monthly payment. N = 180 (15x12); I/Y = 2.85/12 = 0.2375; PV = -365,000; FV = 0; CPT PMT. PMT = $2,494.37 Next, find the principal balance at the beginning of the thirty-fourth month. That is, at time t = 33. N = 33; I/Y = 0.2375; PV = -365,000; PMT = 2494.37; CPT FV. Loan Balance = $309,200.63. Interest portion of the 34th payment = 0.2375% x 309,200.63 = $734.35 Principal Component = $2494.37 - $734.35 = $1,760.02

You borrow $275,000 to purchase a home. The terms of the loan call for monthly payments over 30 years at a mortgage rate of 3.75 percent. What percentage of your first 36 months' total payments go toward interest? 48 percent 74 percent 62 percent 66 percent

First, determine the monthly payments: N = 360; I/Y = 3.75/12 = 0.3125; PV = - 275,000; FV = 0; CPT = PMT. PMT = $1,273.57 After 36 payments, the loan balance is determined as follows: N = 36; I/Y = 0.3125; PV = -275000; PMT = 1,273.57; CPT FV. FV = $259,243.97 Thus, out of the total amount paid of 1,273.57x36 = $45,848.52, the amount that has gone toward principal repayment = 275000 - 259,243.97 = $15,756.03. The rest is interest. Total interest paid = 45,848.52 - 15,756.03 = $30,092.49 Percentage that is interest = (30092.49/45,848.52)x(100%) = 65.63 percent

You are planning to invest an amount of money today to fund your child's education. Your child is twelve years old today. You estimate that she will need $30,000 per year for four years to pay for her college expenses. The first of these $30,000 annual payments will be made when she turns eighteen. If you have found an investment that has a rate of return of 8 percent, how much should you invest today to fund your child's college education?

First, set up your time line accurately. Today is time t = 0. Your child is twelve years old. The day she turns eighteen will be time t = 6. Since the first payment occurs at this time, the annuity's time zero occurs at t = 5. Determine the "present value" of the annuity at time t = 5. N = 4; I/Y = 8; PMT = 30000; FV = 0 CPT PV. PV = $99,363.81 Now, find the value of this $99,363.81 amount at t = 0. N = 5; I/Y = 8; PMT = 0; FV = 99363.81; CPT PV; PV = $67,625.34 Thus, you need to invest $67,625.34 today to fund your child's college education. If you wait till your child turns 17 to fund her education, you will need to invest $99,363.81 at that time, assuming the same investment instrument is available to you then.

1. You just received a $5,000 gift from your grandmother. You have decided to save this money so that you can gift it to your grandchildren 50 years from now. How much additional money will you have to gift to your grandchildren if you can earn an average of 7.5 percent instead of just 7 percent on your savings?

Future value = $5,000 ×(1 + .075)50 = $185,948.73 Future value = $5,000 ×(1 + .07)50 = $147,285.13 Difference = $185,948.73 - 147,285.13 = $38,663.60

1. You own a classic car that is currently valued at $64,000. If the value increases by 2.5 percent annually, how much will the car be worth 15 years from now?

PV = - $64,000; I/Y = 2.5; N = 15; PMT = 0; CPT FV. FV = 92,691.08 Future value = $64,000 ×(1 + .025)15 = $92,691.08

You just took up a 30-year mortgage loan of $330,000 to buy your dream home, at a mortgage rate of 3.50 percent. You immediately decided that you will pay an additional amount of $620 (you prefer this to a 15-year mortgage because of its flexibility) every month to pay off the loan earlier. If you are able to do this each month, by how many years will you shorten the length of time it will take to pay off your loan?

N = 360; I/Y = 3.5/12 = 0.291666667; PV = -330,000; FV = 0; CPT PMT. PMT = $1,481.84747 You have decided to add $620 each month to this monthly payment. Thus, new monthly payment = 1481.84747 + 620 = $2,101.85 Calculate the number of months it will take to pay off your loan, now. I/Y = 0.291666667; PV = -330,000; FV = 0; PMT = 2,101.85.85; CPT N. N = 210.26 You have shortened the length of time by 360 - 210.26 = 149.74 = 149.74/12 = 12.48 years.

Your business finance course has motivated you to begin investing for retirement in your company's 401K plan. Your first $370 monthly investment will be made one month from today and you plan to retire 43 years from today. How much more will you have to invest each month, if you wait for 15 years before starting to invest to end up with the same amount of money at retirement? Assume a rate of return of 0.60 percent per month for your investments.

N = 516 (43x12); I/Y = 0.60; PV = 0; PMT = -370; CPT FV. FV = $1,289,187.68 If you wait 15 years before starting to invest, you have 28 years to retirement. N = 336 (28x12); I/Y = 0.60; PV = 0; FV = -1,289,187.68; CPT PMT. PMT = $1,196.81 Now, you need to save $1,196.81 per month, instead of $370 per month, to obtain the same amount of $1,289,187.68. The additional amount needed per month = 1196.81 - 370 = $826.81

Your employer contributes $82 a week to your retirement plan. Assume you work for your employer for 30 years and the applicable interest rate is 7.8 percent. Given these assumptions, what will this employee benefit amount to on the day you leave the company? (Assume exactly 52 weeks in a year).

N = 52x30 = 1,560; I/Y = 7.8/52 = 0.15; PV = 0; PMT = 82; CPT FV. FV = -511,846.82

You just bought a used Camry for $17,927. You have decided to borrow the entire purchase price from your dealer at an interest rate of 5.80 percent. The loan terms call for equal monthly payments over five years. Calculate your monthly payment amount.

N = 60; I/Y = 5.80/12 = 0.4833333; FV = 0; PV = -17,927; CPT PMT. PMT = 344.91

You want to borrow $52,700 and can afford monthly payments of $1,041 for 60 months, but no more. Assume monthly compounding. What is the highest APR rate you can afford?

N = 60; PV = - 52,700; FV = 0; PMT = 1,041; CPT I/Y. I/Y = 0.574870576. APR = 0.57487x12 = 6.898 percent.

1. What is the future value of $11,600 invested for 17 years at 7.25 percent compounded annually?

N=17; PV = -$11,600; PMT = 0; I/Y = 7.25; CPT FV. FV = $38,125.20 Future value = $11,600 ×(1 + .0725)17 = $38,125.20

1. Some time ago, Tracie purchased 11 acres of land costing $77,900. Today, that land is valued at $54,800. How long has she owned this land if the price of the land has been decreasing by 3.5 percent per year? A. 11.33 years B. 9.08 years C. 9.87 years D. 10.29 years E. 12.08 years

PV = -$77,900; FV = $54,800; I/Y = -3.5; PMT = 0. CPT N N = 9.87 $54,800 = $77,900 ×[1 + (-.035)]t; t = 9.87 years

You plan on taking an Asian vacation 7 years from today. The vacation is estimated to cost $15,300 at the time of traveling, and you have decided to invest in an investment instrument that pays 7.2 percent per year, to fund it. How much should you invest today to achieve your objective?

PV = 15,300/1.0727 = $9,404.33

An insurance company is trying to sell you an investment policy that will pay you and your heirs $90,000 per year forever. If the required return on this investment is 6.0 percent, how much will you pay for the policy?

PVperpetuity = C/r = 90000/0.06 = $1,500,000

1. Your father invested a lump sum 33 years ago at 4.25 percent interest. Today, he gave you the proceeds of that investment which totaled $51,480.79. How much did your father originally invest?

Present value = $51,480.79/(1 + .0425)33 = $13,035.72

You are considering two projects with the following cash flows: Project YProject X Year 1$9,500$6,000 Year 2$9,000$6,900 Year 3$6,900$9,000 Year 4$6,000$9,500 Which one of the following statements is true concerning the two projects given a positive discount rate?

Project Y has both a higher present value and a higher future value than project X.

A microfinance company in a developing country charges petty traders interest rate of 7.5 percent per month. What is the effective annual rate being charged the petty traders?

Reffective = (1 + 0.075)12 - 1 = 1.3818 = 138.18 percent

What is the effective annual rate for a stated APR of 12.3 percent with weekly compounding?

Reffective = (1 + 0.123/52)52- 1 = 0.1307 = 13.07 percent

You are going to receive $34,090 per year for five years. The payments will be received at the beginning of each year, with the first year's payment coming in today. If you plan to invest these amounts, immediately you receive them, in an account that pays interest rate of 8.1 percent, how much will be in your account five years from today?

Set your calculator to BGN mode for annuity due. N = 5; I/Y = 8.1; PV = 0; PMT = - 34,090; CPT FV. FV = 216,623.3158 Alternatively, leave your calculator in END mode and find the FV. You will obtain 200,391.5965. Then, multiply this amount by 1.081; that is, (1 + r). You will get 200,391.5965*(1.081) = 216,623.3158

You have just won a state lottery! You have the option of receiving equal annual payments of $220,000 for 30 years, or a lump sum amount today. The acceptable interest rate is 5.5 percent. If the state offers you a one-time payment of $3.4 million today, should you accept it?

The present value of the annual payments is determined as follows: N = 30; I/Y = 5.5; PMT = 220,000; FV = 0; CPT PV. PV = $3,197,423.938. Since this amount is less than the $3.4 million being offered, you should accept the offer!

If the present value of the cash flow below, discounted using an interest rate of 6 percent, is $30,000, what is the amount at time t = 3? Time (t) Cash Flow ($) 1 11,000 2 7,000 3 ??? 4 10,000

The way to approach this type of problem is to find the present value of each of the known cash flows, add them up to come up with the total present value of all the known cash flows. Then subtract this value from the present value of all the cash flows - known and unknown - given to you in the question. The result is the present value of the missing cash flow. Armed with this, you can now find that cash flow whose present value you have just determined. Present value of the known cash flows is given by: PVknown = 11000/1.06 + 7000/(1.06)2 + 10000/(1.06)4 = $24,528.27 Thus, the present value of the missing cash flow = 30,000 - 24528.27 = $5,471.73 So, what amount sitting at time t = 3 will have a present value of $5,471.73. given a discount rate of 6 percent? N = 3; PV = 5471.73; I/Y = 6; PMT = 0; CPT FV FV = $6,516.92 (missing cash flow)

Ten years from today, you will receive the first of 16 annual equal amounts of $4000. Using a discount rate of 6 percent, determine the present value of these payments (that is, the value today).

This is a two-stage problem in which you first carve out an ordinary annuity problem with its time zero sitting nine years from today and the first annuity amount sitting ten years from today. In this first stage, apply the usual method to determine the value of the annuity at time t = 9 (N=16; I/Y = 6; PMT = 4000; FV = 0; CPT PV). You should obtain a value of $40,423.58. In the second stage, recognize that the answer determined in stage 1 above is the value of all the sixteen payments at time t = 9. Now find the value of that "future amount" at t = 0. N = 9; PMT = 0; I/Y = 6; FV = 40,423.58; CPT PV. PV = $23,926.65

You are celebrating your 22nd birthday today. You have decided to start investing toward your retirement beginning one month from today. For the first twenty years, you will invest $400 every month. During the next ten years, you will increase your contributions to $900 per month. For the remainder of your working life until you retire at age 65, you plan to invest $1,400 every month. If your investments earn a rate of return of 8.6 percent throughout your working life, how much will be in your retirement account on the day you retire?

Use the CF system to find the NPV of your investments. CF0 = 0; C01 = 400; F01 = 240; C02 = 900; F02 = 120; C03 = 1400; F03 = 156; NPV. I = 8.6/12 = 0.716666667; CPT. NPV 68,815.61. Then, find the future value of this amount. FV = 68,815.61(1.0071666667)516 = 2,741,450

Which one of the following statements related to loan interest rates is correct?

When comparing loans you should compare the effective annual rates.

You are going to loan a friend $20,000 for one year at an interest rate of 9.5 percent, compounded annually. How much additional interest could you have earned if you had compounded the rate continuously rather than annually?

With interest compounded annually, effective annual rate = 9.5 percent and interest for one year = 0.095*20000 = $1,900. Effective annual rate with interest compounded continuously = e0.095 - 1 = 9.9658855 percent. Interest received in one year = 0.099658855*20000 = $1,993.18 Additional interest = 1993.18 - 1900 = $93.18

1. At 6 percent interest, how long would it take to quadruple your money? A. 26.55 years B. 16.64 years C. 18.87 years D. 23.79 years E. 20.01 years

You can choose any amount as PV. Then, FV is just four times that amount. Just remember your signs! PV = 100; FV = - 400; I/Y = 6; PMT = 0. CPT N N = 23.79. $4 = $1 ×(1 + .06)t; t = 23.79 years

1. Today is your twenty-second birthday. This morning, you receive $25,000 gift from your grandfather. You immediately invest this amount in an S&P 500 Index fund. Your twin brother also receives $25,000 from your grandfather but does not know about stock market investment and puts his money in a five-year bank certificate of deposit that pays him 2 percent per year. At the end of the five-year period, he decides to invest the proceeds of his certificate of deposit account in the S&P 500 Index fund after observing how well your investment is performing. Both of you plan to withdraw the proceeds of your investment when you turn fifty-five. If the S&P 500 returns 9 percent per year throughout your investment period, how much more will you have than your twin brother?

Your brother: After five years, the CD account will have 25000x(1.02)5 = $27,602. This amount will then be invested in the S&P 500 fund for 28 years (from age 27 till 55). The future value at age 55 is given as follows: 27602x(1.09)28 = $308,325. You: The future value after 33 years in the S&P 500 fund is equal to 25000x(1.09)33 = $429,550. Your amount exceeds your brother's by 429550 - 308325 = $121,225.

You have just purchased your dream home for $400,000. You came up with 20 percent for down payment and borrowed the rest from a mortgage lender. The terms of the mortgage loan are as follows: Thirty-year mortgage with no prepayment penalty. The mortgage interest rate is 3.75 percent. a) Determine your monthly payment on the loan. b) If you make your monthly payments on time, what will be your loan balance after making your 60thpayment? c) After making the 60th payment, you decide to refinance your loan. Your new loan is a fifteen-year mortgage with interest rate of 3.00 percent. What is your new monthly mortgage payment, assuming zero refinance cost?

a) Down payment = 0.2x400000 = $80,000. Amount borrowed = 400000 - 80000 = $320,000 N = 360; I/Y = 3.75/12 = 0.3125; FV = 0; PV = - 320000 CPT PMT PMT = $1481.97 b) After making 60 payments, you now have 300 payments more to make. Thus, the loan balance is the value of the 300 payments left at time t = 60. N = 300; I/Y = 0.3125; FV = 0; PMT = 1481.97; CPT PV PV = $288,247 We could have obtained the correct answer by asking ourselves how much we need to pay off the loan at time t = 60 right after making the 60th payment. In other words, what bulk amount sitting at t=60 (FV) will make the cash flows equivalent to the original setup? N = 60; I/Y = 0.3125; PMT = 1481.97; PV = - 320000 CPT FV FV = 288247 c) N = 180; PV = - 288,247; FV = 0; I/Y = 3/12 = 0.25; CPT PMT. PMT = $1,990.58

You borrowed $15,000 at an interest rate of 9 percent per year. The terms of the loan call for equal annual payment for four years. a) Determine the annual payment. b) Construct an amortization table c) What percentage of the first payment goes toward interest? d) What percentage of the third payment goes toward principal?

a) N = 4; I/Y = 9; FV = 0; PV = 15,000 CPT PMT Annual Payment = $4,630.03 b) Column 1 Column 2 = (6) after first Column 3 Column 4 r x (2) Column 5 (3) - (4) Column 6 (2) - (5) Year Beginning Loan Balance Total Payment Interest Paid Principal Paid Ending Loan Balance 1 15000 4630.03 1350 3280.03 11719.97 2 11719.97 4630.03 1054.80 3575.23 8144.74 3 8144.74 4630.03 733.03 3897.00 4247.74 4 4247.74 4630.03 382.30 4247.73 0.01 zero c) 1350/4630.03 = 29.16% of the first payment goes toward interest Thus, 70.84% goes toward principal. d) 3897/4630.03 = 84.17% of the third payment goes toward principal. Thus 15.83% is interest.

1. You just purchased your first home for $170,000. As a first time home buyer, you took advantage of a government program that allowed you to put zero down. The interest rate on your thirty-year mortgage is 4.25 percent. a) What is your monthly mortgage payment? b) If you had decided to take a fifteen-year mortgage at an interest rate of 3.25 percent, what would have been your monthly mortgage? c) Assume you make all your monthly payments on time. What will be your loan balance after seven years in case (a) and case (b) above? d) How much of your second month's payment goes toward principal in case (a) and in case (b)?

a) PV = - 170000; N = 30x12 = 360; I/Y = 4.25/12 = 0.354167; FV = 0; CPT PMT PMT = $836.30 b) PV = - 170000; N = 15x12 = 180; I/Y = 3.25/12 = 0.2708333; FV = 0; CPT PMT PMT = $1,194.54 ** Your payment is about $358 more each month. However, you will pay off your mortgage in 15 years instead of 30 years. Fifteen years from now, if you had taken the thirty-year mortgage, your loan balance will be $111,169. c) In each case, first calculate your monthly mortgage amount as in a) and b) above. Then, find the present value of the payments left after 7 years. In the thirty-year case: N = 23x12 = 276; I/Y = 4.25/12 = 0.354167; FV = 0; PMT = 836.30; CPT PV. PV = $147,133 In the fifteen-year case: N = 8x12 = 96; I/Y = 3.25/12 = 0.270833; FV = 0; PMT = 1194.54; CPT PV. PV = $100,861 d) This is a loan amortization question. In the thirty-year mortgage case: 0.0425/12*Column2 Column 3 - Column 4 Column 2 - Column 5 Month Beginning Loan Balance Total Payment Interest Paid Principal Paid Ending Loan Balance 1 170000 836.30 602.08 234.22 169,765.78 2 169,765.78 836.30 601.25 235.05 169,530.73 In the fifteen-year case: 0.0325/12*Column2 Column 3 - Column 4 Column 2 - Column 5 Month Beginning Loan Balance Total Payment Interest Paid Principal Paid Ending Loan Balance 1 170000 1194.54 460.42 734.12 169,265.88 2 169,265.88 1194.54 458.43 736.11 168,529.77