Finance Exam 2 study guide

Today you deposit $1000 in an account paying 6% interest. At the end of years 1, 2, & 3 you will deposit $100 in that account. How much will you have at the end of year 4?

$1,599.94 $1000(1.06)^4 + $100(1.06)^3 + $100(1.06)^2 + $100(1.06)^1

You will receive $100 in 1 year, $200 in 2 years & $300 in 3 years. If you can earn a 7.5% rate of interest, what is the present value of this stream of cash flows?

$507.58 $100/(1.075)^1 + $200/(1.075)^2 + $300/(1.075)^3

Compound growth means that value increases after t periods by:

(1 + growth rate)^t

What are valid interest compounding periods?

-Daily -Weekly -Monthly -Annually -Continuously -Quarterly -Semiannually

What are annuities?

-Installment loan payments -Monthly rent payments in a lease

What is the effective annual interest rate on a 9% APR automobile loan that has monthly payments? A. 9.00% B. 9.38% C. 9.81% D. 10.94%

B. 9.38% EAR = [1 + (.09/12)]12 - 1 = .0938, or 9.38%

Approximately how much must be saved for retirement in order to withdraw $100,000 per year for the next 25 years if the balance earns 8% annually, and the first payment occurs one year from now? A. $1,067,477.62 B. $1,128,433.33 C. $1,487,320.09 D. $1,250,000.00

A. $1,067,477.62 PV = $100,000 {(1/.08) - [1/.08(1.08)25]} PV = $1,067,477.62

Miller's Hardware plans on saving $42,000, $54,000, and $58,000 at the end of each year for the next three years, respectively. How much will the firm have saved at the end of the three years if it can earn 4.5% on its savings? A. $160,295.05 B. $158,098.15 C. $167,508.33 D. $165,212.57

A. $160,295.05 FV = ($42,000 × 1.0452) + ($54,000 × 1.045) + $58,000 FV = $160,295.05

Prizes are often not "worth" as much as claimed. Place a value on a prize of $5,000,000 that is to be received in equal payments over 20 years, with the first payment beginning today. Assume an interest rate of 7%. A. $2,833,898.81 B. $2,911,015.68 C. $2,609,144.14 D. $2,738,304.13

A. $2,833,898.81 Annual payment = $5,000,000/20 = $250,000 PV = ($250,000 {(1/.07) - [1/.07(1.07)20]}) × (1.07) PV = $2,833,898.81

You're ready to make the last of four equal, annual payments on a $1,000 loan with a 10% interest rate. If the amount of the payment is $315.47, how much of that payment is accrued interest? A. $28.68 B. $31.55 C. $100.00 D. $315.47

A. $28.68 $315.47 - ($315.47/1.1) = $28.68

What is the present value of a four-year annuity of $100 per year that begins 2 years from today if the discount rate is 9%? A. $297.22 B. $323.97 C. $356.85 D. $272.68

A. $297.22 PV = {$100[(1/.09) - 1/.09(1.09)4]}/1.09 PV = $297.22

How much must be saved at the end of each year for the next 10 years in order to accumulate $50,000, if you can earn 9% annually? Assume you contribute the same amount to your savings every year. A. $3,291.00 B. $3,587.87 C. $4,500.33 D. $4,587.79

A. $3,291.00 Payment = $50,000/[(1.0910 - 1)/.09] Payment = $3,291.00

How much must be invested today in order to generate a 5-year annuity of $1,000 per year, with the first payment 1 year from today, at an interest rate of 12%? A. $3,604.78 B. $3,746.25 C. $4,037.35 D. $4,604.78

A. $3,604.78 PV = $1,000{(1/.12) - [1/.12(1.125)]} PV = $3,604.78

What is the present value of the following payment stream, discounted at 8% annually: $1,000 at the end of year 1, $2,000 at the end of year 2, and $3,000 at the end of year 3? A. $5,022.10 B. $5,144.03 C. $5,423.87 D. $5,520.00

A. $5,022.10 PV = $1,000/1.08 + $2,000/1.082 + $3,000/1.083 PV = $5,022.10

How much more would you be willing to pay today for an investment offering $10,000 in 4 years rather than in 5 years? Your discount rate is 8%. A. $544.47 B. $681.48 C. $740.74 D. $800.00

A. $544.47 Difference = FV/(1 + r)t - 1 - FV/(1 + r) Difference = $10,000/1.084 - $10,000/1.085 Difference = $544.47

Your car loan requires payments of $200 per month for the first year and payments of $400 per month during the second year. The annual interest rate is 12% and payments begin in one month. What is the present value of this 2-year loan? A. $6,246.34 B. $6,389.78 C. $6,428.57 D. $6,753.05

A. $6,246.34 PV = {$200 {(1/.01) - [1/.01(1.01)12]}} + ({$400 {(1/.01) - [1/.01(1.01)12]}/1.0112)} PV = $6,246.34

On the day you retire you have $1,000,000 saved. You expect to live another 25 years during which time you expect to earn 6.19% on your savings while inflation averages 2.5% annually. Assume you want to spend the same amount each year in real terms and die on the day you spend your last dime. What real amount will you be able to spend each year? A. $61,334.36 B. $79,644.58 C. $79,211.09 D. $61,931.78

A. $61,334.36 Real rate = (1.0619/1.025) - 1 = .036 $1,000,000 = PMT {(1/.036) - [1/.036(1.036)25]} PMT = $61,334.36

What will be the monthly payment on a home mortgage of $75,000 at 12% interest, to be amortized over 30 years? A. $771.46 B. $775.90 C. $1,028.61 D. $1,034.53

A. $771.46 Payment = $75,000/[(1/.01) - 1/.01(1.01)360] Payment = $771.46

A credit card account that charges interest at the rate of 1.25% per month would have an annually compounded rate of _____ and an APR of ____. A. 16.08%; 15.00% B. 14.55%; 16.08% C. 12.68%; 15.00% D. 15.00%; 14.55%

A. 16.08%; 15.00% EAR = (1 + .0125)12 - 1 = .1608, or 16.08% APR = 1.25% × 12 = 15.00%

Given a set future value, which of the following will contribute to a lower present value? A. Higher discount rate B. Fewer time periods C. Less frequent discounting D. Lower discount factor

A. Higher discount rate

What is the relationship between an annually compounded rate and the annual percentage rate (APR) which is calculated for truth-in-lending laws for a loan requiring monthly payments? A. The APR is lower than the annually compounded rate. B. The APR is higher than the annually compounded rate. C. The APR equals the annually compounded rate. D. The answer depends on the interest rate.

A. The APR is lower than the annually compounded rate.

Inflation can be defined as

An overall general rise in prices

What is the annually compounded rate of interest on an account with an APR of 10% and monthly compounding? A. 10.00% B 10.47% . C. 10.52% D. 11.05%

B 10.47% EAR = [1 + (.10/12)] 12 - 1 = .1047, or 10.47%

How much more is a perpetuity of $1,000 worth than an annuity of the same amount for 20 years? Assume an interest rate of 10% and cash flows at the end of each period. A. $297.29 B. $1,486.44 C. $1,635.08 D. $2,000.00

B. $1,486.44 PVPerpetuity = $1,000/.10 = $10,000 PVAnnuity = $1,000[1/.10 - 1/.10(1.10)20] PVAnnuity = $8,513.56 Difference = $10,000 - 8,513.56 = $1,486.44

A car dealer offers payments of $522.59 per month for 48 months on a $25,000 car after making a $4,000 down payment. What is the loan's APR? A. 6% B. 9% C. 11% D. 12%

B. 9% $25,000 - 4,000 = $522.59 {(1/r) - [1/r(1 + r)48]} Using a financial calculator, r = .0075 APR = .0075 × 12 APR = .09, or 9%

You will be receiving cash flows of: $1,000 today, $2,000 at end of year 1, $4,000 at end of year 3, and $6,000 at end of year 5. What is the present value of these cash flows at an interest rate of 7%? A. $9,731.13 B. $10,412.27 C. $10,524.08 D. $11,524.91

B. $10,412.27 PV = FV/(1 + r)t PV = $1,000 + $2,000/1.071 + $4,000/1.073 + $6,000/1.075 PV = $10,412.27

What is the present value of $100 to be deposited today into an account paying 8%, compounded semiannually for 2 years? A. $85.48 B. $100.00 C. $116.00 D. $116.99

B. $100.00

How much interest can be accumulated during one year on a $1,000 deposit paying continuously compounded interest at an APR of 10%? A. $100.00 B. $105.17 C. $110.50 D. $115.70

B. $105.17 Interest = $1,000 × e.1 - $1,000 Interest = $1,000 × 1.10517 - $1,000 Interest = $105.17

How much interest will be earned in an account into which $1,000 is deposited for one year with continuous compounding at a 13% rate? A. $130.00 B. $138.83 C. $169.00 D. $353.34

B. $138.83 Interest = $1,000(e.13) - $1,000 = $138.83

What is the present value of your trust fund if you have projected that it will provide you with $50,000 on your 30th birthday (7 years from today) and it earns 10% compounded annually? A. $25,000.00 B. $25,657.91 C. $28,223.70 D. $29,411.76

B. $25,657.91 PV = FV/(1 + r)t PV = $50,000/1.107 PV = $25,657.91

A corporation has promised to pay $1,000 20 years from today for each bond sold now. No interest will be paid on the bonds during the 20 years, and the bonds are discounted at an interest rate of 7%, compounded semiannually. Approximately how much should an investor pay for each bond? A. $70.00 B. $252.57 C. $629.56 D. $857.43

B. $252.57 PV = FV/(1 + r)t PV = $1,000/[1 + (.07/2)]20 × 2 PV = $252.57

Approximately how much should be accumulated by the beginning of retirement to provide a $2,500 monthly check that will last for 25 years, during which time the fund will earn 6% interest with monthly compounding? A. $361,526.14 B. $388,017.16 C. $402,766.67 D. $414,008.24

B. $388,017.16 Monthly interest rate = .06/12 = .005 PV = $2,500 {(1/.005) - [1/.005(1.005)12 × 25]} PV = $388,017.16

The salesperson offers, "Buy this new car for $25,000 cash or, with an appropriate down payment, pay $500 per month for 48 months at 8% interest." Assuming that the salesperson does not offer a free lunch, calculate the "appropriate" down payment. A. $1,000.00 B. $4,519.04 C. $5,127.24 D. $8,000.00

B. $4,519.04 PV = $500 × {[1/(.08/12)] - [1/(.08/12)(1 + (.08/12)48)]} PV = $20,480.96 Down payment = $25,000 - 20,480.96 = $4,519.04

The present value of an annuity stream of $100 per year is $614 when valued at a 10% rate. By approximately how much would the value change if these were annuities due? A. $10 B. $61.40 C. $10 × Number of years in annuity stream D. $6.14 × Number of years in annuity stream

B. $61.40 PVAD = PVOA × (1 + r) Difference = [PVOA × (1 + r)] - PVOA Difference = $614(1.1) - $614 = $61.40

How much can be accumulated for retirement if $2,000 is deposited annually, beginning 1 year from today, and the account earns 9% interest compounded annually for 40 years? A. $87,200.00 B. $675,764.89 C. $736,583.73 D. $802,876.27

B. $675,764.89 FV = $2,000 {[(1 + .09)40 - 1]/.09} FV = $675,764.89

How much interest is earned in just the third year on a $1,000 deposit that earns 7% interest compounded annually? A. $70.00 B. $80.14 C. $105.62 D. $140.00

B. $80.14 $1000.00 × (1.07)2 = $1,144.90 after 2 years $1,144.90 × .07 = $80.14

How long must one wait (to the nearest year) for an initial investment of $1,000 to triple in value if the investment earns 8% compounded annually? A. 9.81 years B. 14.27 years C. 22.01 years D. 25.00 years

B. 14.27 years

After reading the fine print in your credit card agreement, you find that the "low" interest rate is actually an 18% APR, or 1.5% per month. What is the effective annual rate? A. 18.47% B. 19.56% C. 18.82% D. 19.41%

B. 19.56% EAR = 1.01512 - 1 = .1956, or 19.56%

If the future value of an annuity due is $25,000 and $24,000 is the future value of an ordinary annuity that is otherwise similar to the annuity due, what is the implied discount rate? A. 1.04% B. 4.17% C. 5.00% D. 8.19%

B. 4.17% FVAD = FVOA × (1 + r) $25,000 = $24,000 × (1 + r) r =.0417, or 4.17%

If inflation in Wonderland averaged about 3% per month in 2013, what was the annual rate of inflation? A. 36.00% B. 42.58% C. 40.09% D. 41.27%

B. 42.58% (1.03)12 - 1 = .4258, or 42.58%

What is the expected real rate of interest for an account that offers a 12% nominal rate of return when the rate of inflation is 6% annually? A. 5.00% B. 5.66% C. 6.00% D. 9.46%

B. 5.66% 1 + real interest rate = (1 + nominal interest rate)/(1 + inflation) 1 + real interest rate = 1.12/1.06 Real interest rate = 5.66%

Your retirement account has a current balance of $50,000. What interest rate would need to be earned in order to accumulate a total of $1,000,000 in 30 years, by adding $6,000 annually? A. 5.02% B. 7.24% C. 9.80% D. 10.07%

B. 7.24% Financial calculator: n = 30; PV = -50,000; PMT = -6,000; FV = 1,000,000; CPT i = 7.24%

In calculating the present value of $1,000 to be received 5 years from today, the discount factor has been calculated to be .7008. What is the apparent interest rate? A. 5.43% B. 7.37% C. 8.00% D. 9.50%

B. 7.37% FV = PV(1 + r)t 1 = .7008(1 + r)5 r = .0737, or 7.37%

If a borrower promises to pay you $1,900 nine years from now in return for a loan of $1,000 today, what effective annual interest rate is being offered if interest is compounded annually? A. 5.26% B. 7.39% C. 9.00% D. 10.00%

B. 7.39% FV = PV × (1 + r)t $1,900 = $1,000 × (1 + r)9 r = 1.91/9 - 1 r = .0739, or 7.39%

Would a depositor prefer an APR of 8% with monthly compounding or an APR of 8.5% with semiannual compounding? A. 8.0% with monthly compounding B. 8.5% with semiannual compounding C. The depositor would be indifferent. D. The time period must be known to select the preferred account.

B. 8.5% with semiannual compounding EAR = [1 + (.08/12)]12 - 1 = 8.30% EAR = [1 + (.085/2)]2 - 1 = 8.68% The depositor will prefer the option with the higher EAR (effective annual rate).

Which one of the following will increase the present value of an annuity, other things equal? A. Increasing the interest rate B. Decreasing the interest rate C. Decreasing the number of payments D. Decreasing the amount of the payment

B. Decreasing the interest rate

Which one of the following factors is fixed and thus cannot change for a specific perpetuity? A. Present value B. Payment amount C. Interest rate D. Discount rate

B. Payment amount

The APR on a loan must be equal to the effective annual rate when: A. compounding occurs monthly. B. compounding occurs annually. C. the loan is for less than one year. D. the loan is for more than one year.

B. compounding occurs annually.

Assume you are making $989 monthly payments on your amortized mortgage. The amount of each payment that is applied to the principal balance: A. decreases with each succeeding payment. B. increases with each succeeding payment. C. is constant throughout the loan term. D. fluctuates monthly with changes in market interest rates.

B. increases with each succeeding payment.

The concept of compound interest refers to: A. earning interest on the original investment. B. payment of interest on previously earned interest. C. investing for a multiyear period of time. D. determining the APR of the investment.

B. payment of interest on previously earned interest.

Three thousand dollars is deposited into an account paying 10% annually to provide three annual withdrawals of $1,206.34 beginning in one year. How much remains in the account after the second payment has been withdrawn? A. $1,326.97 B. $1,206.34 C. $1,096.69 D. $587.32

C. $1,096.69 FVYear 1 = PV(1 + r) - Withdrawal FVYear 1 = $3,000(1.1) - $1,206.34 FVYear 1 = $2,093.66 FVYear 2 = FVYear 1 (1 + r) - Withdrawal FVYear 2 = $2,093.66(1.1) - $1,206.34 FVYear 2 = $1,096.69

You invested $1,200 three years ago. During the three years, you earned annual rates of return of 4.8%, 9.2%, and 11.6%. What is the value of this investment today? A. $1,498.08 B. $1,512.11 C. $1,532.60 D. $1,549.19

C. $1,532.60 FV = PV(1 + r)t FV = PV(1 + r)t (1 + r)t (1 + r)t FV = $1,200(1.048)1 (1.092)1 (1.116)1 FV = $1,532.60

How much interest will be earned in the next year on an investment paying 12% compounded annually if $100 was just credited to the account for interest? A. $88 B. $100 C. $112 D. $200

C. $112 The investment will again pay $100 plus interest on the previous interest: $100 × 1.12 = $112

A loan officer states, "Thousands of dollars can be saved by switching to a 15-year mortgage from a 30-year mortgage." Calculate the difference in payments on a 30-year mortgage at 9% interest versus a 15-year mortgage with 8.5% interest. Both mortgages are for $100,000 and have monthly payments. What is the difference in total dollars that will be paid to the lender under each loan? (Round the monthly payment amounts to 2 decimal places.) A. $89,211 B. $98,406 C. $112,410 D. $124,300

C. $112,410 $100,000 = PMT([1/(.09/12)] - 1/{(.09/12)[1 + (.09/12)]30 × 12}) PMT = $804.62 $100,000 = PMT([1/(.085/12)] - 1/{(.085/12)[1 + (.085/12)]15 × 12}) PMT = $984.74 Total difference = ($804.62 × 12 × 30) - ($984.74 × 12 × 15) = $112,410

What is the present value of a five-period annuity of $3,000 if the interest rate per period is 12% and the first payment is made today? A. $9,655.65 B. $10,814.33 C. $12,112.05 D. $13,200.00

C. $12,112.05 PVAD = PVOA × (1 + r) PVAD = {$3,000[1/.12 - 1/.12(1.12)5]} × 1.12 PVAD = $12,112.05

With $1.5 million in an account expected to earn 8% annually over the retiree's 30 years of life expectancy, what annual annuity can be withdrawn, beginning today? A. $112,148.50 B. $120,000.00 C. $123,371.44 D. $133,241.15

C. $123,371.44 $1,500,000 = PmtOA {(1/.08) - [1/.08(1.08)30]} PMTOA = $133,241.15 PMTAD = PMTOA/(1 + r) PMTAD = $133,241.15/1.08 PMTAD = $123,371.44

What is the future value of $10,000 on deposit for 5 years at 6% simple interest? A. $7,472.58 B. $10,303.62 C. $13,000.00 D. $13,382.26

C. $13,000.00 FV = PV + (PV × r × t) ($10,000) + [($10,000 × .06) × 5] = $13,000.00

How much will accumulate in an account with an initial deposit of $100, and which earns 10% interest compounded quarterly for 3 years? A. $107.69 B. $133.10 C. $134.49 D. $313.84

C. $134.49

Your real estate agent mentions that homes in your price range require a payment of $1,200 per month for 30 years at 9% interest. What is the size of the mortgage with these terms? A. $128,035.05 B. $147,940.29 C. $149,138.24 D. $393,120.03 PV = $1,200[(1/.0075) - 1/.0075(1.0075)360] PV = $149,138.24

C. $149,138.24

$50,000 is borrowed, to be repaid in three equal, annual payments with 10% interest. Approximately how much principal is amortized with the first payment? A. $2,010.60 B. $5,000.00 C. $15,105.74 D. $20,105.74

C. $15,105.74 Payment = $50,000/[1/.1 - 1/.1(1.1)3] Payment = $20,105.74 Principal payment = $20,105.74 - ($50,000 × .1) Principal payment = $15,105.74

How much must be deposited today in an account earning 6% annually to accumulate a 20% down payment to use in purchasing a car one year from now, assuming that the car's current price is $20,000, and inflation will be 4%? A. $3,774.61 B. $3,782.20 C. $3,924.53 D. $4,080.08

C. $3,924.53 Down payment needed = ($20,000 × 1.04) × .2 = $4,160 PV = FV/(1 + r)t PV = $4,160/(1.06) PV = $3,924.53

A perpetuity of $5,000 per year beginning today is said to offer a 15% interest rate. What is its present value? A. $33,333.33 B. $37,681.16 C. $38,333.33 D. $65,217.39

C. $38,333.33 PV = $5,000 + FV/r PV = $5,000 + $5,000/.15 PV = $5,000 + $5,000/.15 PV = $38,333.33

Lester's just signed a contract that will provide the firm with annual cash inflows of $28,000, $35,000, and $42,000 over the next three years with the first payment of $28,000 occurring one year from today. What is this contract worth today at a discount rate of 7.25%? A. $88,311.08 B. $89,423.91 C. $90,580.55 D. $91,341.41

C. $90,580.55 PV = $28,000/1.0725 + $35,000/1.07252 + $42,000/1.07253 PV = $90,580.55

You are considering the purchase of a home that would require a mortgage of $150,000. How much more in total interest will you pay if you select a 30-year mortgage at 5.65% rather than a 15-year mortgage at 4.9%? (Round the monthly payment amount to 2 decimal places.) A. $86,311.18 B. $78,487.92 C. $99,595.80 D. $102,486.68

C. $99,595.80 $150,000 = PMT([1/(.0565/12)] - 1/{(.0565/12)[1 + (.0565/12)]30 × 12}) PMT = $865.85 $150,000 = PMT([1/(.049/12)] - 1/{(.049/12)[1 + (.049/12)]15 × 12}) PMT = $1,178.39 Total difference = ($865.85 × 12 × 30) - ($1,178.39 × 12 × 15) = $99,595.80

"Give me $5,000 today and I'll return $10,000 to you in 5 years," offers the investment broker. To the nearest percent, what annual interest rate is being offered? A. 12.29% B. 13.67% C. 14.87% D. 12.84%

C. 14.87% FV = PV(1 + r)t $10,000 = $5,000(1 + r)5 r = 21/5 - 1 r = .1487, or 14.87%

What is the APR on a loan that charges interest at the rate of 1.4% per month? A. 10.20% B. 14.00% C. 16.80% D. 18.16%

C. 16.80% APR = 1.4% × 12 = 16.80%

What APR is being earned on a deposit of $5,000 made 10 years ago today if the deposit is worth $9,848.21 today? The deposit pays interest semiannually. A. 3.56% B. 6.76% C. 6.89% D. 7.12%

C. 6.89% FV = PV (1 + r)t $9,848.21 = $5,000 [1 + (r/2)]10 × 2 r = 6.89%

What is the minimum nominal rate of return that you should accept if you require a 4% real rate of return and the rate of inflation is expected to average 3.5% during the investment period? A. 7.36% B. 7.50% C. 7.64% D. 8.01%

C. 7.64% 1 + nominal rate = (1 + real rate)(1 + inflation rate) Nominal rate = (1.04 × 1.035) - 1 Nominal rate = 7.64%

A furniture store is offering free credit on purchases over $1,000. You observe that a big-screen television can be purchased for nothing down and $4,000 due in one year. The store next door offers an identical television for $3,650 but does not offer credit terms. Which statement below best describes the cost of the "free" credit? A. 8.75% B. 9.13% C. 9.59% D. 0%

C. 9.59% FV = PV(1 + r)t $4,000 = $3,650(1 + r) r = .0959, or 9.59%

How many monthly payments remain to be paid on an 8% mortgage with a 30-year amortization and monthly payments of $733.76, when the balance reaches one-half of the $100,000 mortgage? A. Approximately 268 payments B. Approximately 180 payments C. Approximately 91 payments D. Approximately 68 payments

C. Approximately 91 payments PV = PMT [(1/r) - 1/r(1 + r)t] $50,000 = $733.76{[1/(.08/12)] - 1/(.08/12) [1 + (.08/12)]t} t ≈ 91

A cash-strapped young professional offers to buy your car with four, equal annual payments of $3,000, beginning 2 years from today. Assuming you're indifferent to cash versus credit, that you can invest at 10%, and that you want to receive $9,000 for the car, should you accept? A. Yes; present value is $9,510.08 B. Yes; present value is $11,372.67 C. No; present value is $8,645.09 D. No; present value is $7,461.17

C. No; present value is $8,645.09 PV = $3,000{(1/.1) - [1/(.1 × 1.14)]}/1.1 PV = $8,645.09

What happens over time to the real cost of purchasing a home if the mortgage payments are fixed in nominal terms and inflation is in existence? A. The real cost is constant. B. The real cost is increasing. C. The real cost is decreasing. D. The price index must be known to answer this question.

C. The real cost is decreasing.

Real interest rates: A. always exceed inflation rates. B. can decline to zero but no lower. C. can be negative, zero, or positive. D. traditionally exceed nominal rates.

C. can be negative, zero, or positive.

Other things being equal, the more frequent the compounding period, the: A. higher the annual percentage rate. B. lower the annual percentage rate. C. higher the effective annual interest rate. D. lower the effective annual interest rate.

C. higher the effective annual interest rate.

Assume your uncle recorded his salary history during a 40-year career and found that it had increased 10-fold. If inflation averaged 4% annually during the period, then over his career his purchasing power: A. remained on par with inflation. B. increased by nearly 1% annually. C. increased by nearly 2% annually. D. decreased.

C. increased by nearly 2% annually. FV = PV(1 + r)t 10 = 1(1 + i)40 r = 5.93% Real rate = (1.0593/1.04) - 1 = .0186, or 1.86%

Eighteen years from now, 4 years of college are expected to cost $150,000. How much more must be deposited into an account today to fund this expense if you could only earn 8% rather than the 11% you had hoped to earn on your savings? A. $12,211.18 B. $13,609.21 C. $14,006.41 D. $14,614.03

D. $14,614.03 Additional deposit = $150,000/1.0818 - $150,000/1.1118 Additional deposit = $14,614.03

If $120,000 is borrowed for a home mortgage, to be repaid at 9% interest over 30 years with monthly payments of $965.55, how much interest is paid over the life of the loan? A. $120,000 B. $162,000 C. $181,458 D. $227,598

D. $227,598 Interest = ($965.55 × 12 × 30) - $120,000 = $227,598

Assume the total expense for your current year in college equals $20,000. How much would your parents have needed to invest 21 years ago in an account paying 8% compounded annually to cover this amount? A. $952.46 B. $1,600.00 C. $1,728.08 D. $3,973.11

D. $3,973.11 PV = $20,000/(1.08)21 PV = $3,973.11

What is the discount factor for $1 to be received in 5 years at a discount rate of 8%? A. .4693 B. .5500 C. .6000 D. .6806

D. .6806 PV = FV/(1 + r)t PV = 1/1.085 PV = .6806

What is the APR on a loan with an effective annual rate of 15.26% and weekly compounding of interest? A. 14.35% B. 14.49% C. 13.97% D. 14.22%

D. 14.22% APR = [(1.1526)1/52 - 1] × 52 = .1422, or 14.22%

If the effective annual rate of interest is known to be 16.08% on a debt that has quarterly payments, what is the annual percentage rate? A. 4.02% B. 10.02% C. 14.50% D. 15.19%

D. 15.19% APR = [(1.1608).25 - 1] × 4 APR = .1519, or 15.19%

What will be the approximate population of the United States, if its current population of 300 million grows at a compound rate of 2% annually for 25 years? A. 413 million B. 430 million C. 488 million D. 492 million

D. 492 million FV = PV(1 + r)t FV = 300 million × (1.02)25 FV = 492.2 million ≈ 492 million

Would you prefer a savings account that paid 7% interest compounded quarterly, 6.8% compounded monthly, 7.2% compounded weekly, or an account that paid 7.5% with annual compounding? A. 7% compounded quarterly B. 6.8% compounded monthly C. 7.2% compounded weekly D. 7.5% compounded annually

D. 7.5% compounded annually EAR = [1 + (.07/4)]4 - 1 = .0719, or 7.19% EAR = [1 + (.068/12)]12 - 1 = .0702, or 7.02% EAR = [1 + (.072/52)]52 - 1 = .0746, or 7.46% EAR = APR = 7.5%

Under which of the following conditions will a future value calculated with simple interest exceed a future value calculated with compound interest at the same rate? A. The interest rate is very high. B. The investment period is very long. C. The compounding is annually. D. This is not possible with positive interest rates.

D. This is not possible with positive interest rates.

A stream of equal cash payments lasting forever is termed: A. an annuity. B. an annuity due. C. an installment plan. D. a perpetuity.

D. a perpetuity.

If interest is paid m times per year, then the per-period interest rate equals the: A. effective annual rate divided by m. B. compound interest rate times m. C. effective annual rate. D. annual percentage rate divided by m.

D. annual percentage rate divided by m.

The present value of a perpetuity can be determined by: A. multiplying the payment by the interest rate. B. dividing the interest rate by the payment. C. multiplying the payment by the number of payments to be made. D. dividing the payment by the interest rate.

D. dividing the payment by the interest rate.

An interest rate that has been annualized using compound interest is termed the: A. simple interest rate. B. annual percentage rate. C. discounted interest rate. D. effective annual interest rate.

D. effective annual interest rate.

When an investment pays only simple interest, this means: A. the interest rate is lower than on comparable investments. B. the future value of the investment will be low. C. the earned interest is nontaxable to the investor. D. interest is earned only on the original investment.

D. interest is earned only on the original investment.

Cash flows occurring in different periods should not be compared unless: A. interest rates are expected to be stable. B. the flows occur no more than one year from each other. C. high rates of interest can be earned on the flows. D. the flows have been discounted to a common date.

D. the flows have been discounted to a common date.

An amortizing loan is one in which: A. the principal remains unchanged with each payment. B. accrued interest is paid regularly. C. the maturity of the loan is variable. D. the principal balance is reduced with each payment.

D. the principal balance is reduced with each payment.

What is the future value of a series of $2000 end of year deposits into an IRA account paying 5% interest, over a period of 35 years? --financial calculator needed

FV=$180,640.61 n=35 i=5 PV=0 PMT=2000

TRUE or FALSE The discount factor refers to the present value of a $1 future payment

TRUE

TRUE or FALSE The nominal interest rate can be defined as an interest rate quoted today by a financial institution on a loan or investment, such as an APR or a periodic rate

TRUE

TRUE or FALSE? The time value of money functions that are provided by your financial calculator are also available as functions in an Excel spreadsheet

TRUE

The interest rate per period is most properly defined as

The interest rate that is applied to the current balance every compounding period

The value in t years of an investment made today at interest rate r is called the _______ of your investment

future value

The real interest rate can be defined as

The real change in value of an investment (or a real cost of a loan) after adjustment for inflation

Nominal cash payments should be discounted using a nominal interest rate

True regarding the present value of a stream of cash payments

Real cash payments should be discounted using a real interest rate

True regarding the present value of a stream of cash payments

Joseph signs a contract with a company that will pay him $25,000. Following the principles of the time value of money, Joseph would be best off if he received payment:

at the beginning of the project

Discounting a future value at interest rate "r" over time "t" is termed a _____ calculation

discounted cash-flow

A traditional (non-growing) annuity consists of a _____ stream of cash flows for a fixed period of time

fixed

A perpetuity is a constant stream of cash flows for a _______ period of time

infinite

Calculator keys & their correct functions

n= number of periods i= interest rate expressed as a % PV= Present Value FV= Future Value PMT= Constant recurring payment

Real-world investments often involve many payments received or paid over time. Managers refer to this as a

stream of cash flows

The Annual Percentage Rate (APR) on a loan or investment is properly defined as

the interest rate per period multiplied by the number of compounding periods per year