FIN Unit 6 Quiz

Which one of the following is an ordinary annuity, but not a perpetuity?

$25 paid weekly for 1 year, starting one week from today

At 10 percent interest, how long does it take to triple your money?

$3 = $1 ×(1 + .10)t t = 11.53 years

Sporting Goods charges .85 percent interest per month. What rate of interest are its credit customers actually paying?

EAR = (1 + .0085)12- 1 = .1069, or 10.69 percent

What is the effective annual rate of 8.25 percent compounded quarterly?

EAR = [1 + (.0825 /4)]4- 1 = .0851, or 8.51 percent

Suenette plans to save $600 at the end of Year 1, $800 at the end of Year 2, and $1,000 at the end of Year 3. If she earns 3.4 percent on her savings, how much money will she have saved at the end of Year 3?

FV = ($600 ×1.0342) + ($800 ×1.0341) + $1,000 = $2,468.69

JK Industries just signed a sales contract with a new customer. JK will receive annual payments in the amount of $62,000, $108,000, $135,000, and $150,000 at the end of Years 1 to 4, respectively. What is this contract worth at the end of Year 4 if the firm earns 4.3 percent on its savings?

FV = ($62,000 ×1.0433) + ($108,000 ×1.0432) + ($135,000 ×1.0431) + $150,000 = $478,639.54

Your coin collection contains ten 1949 silver dollars. If your grandparents purchased the coins for their face value when they were new, how much will your collection be worth when you retire in 2065, assuming the coins appreciate at an annual rate of 5.1 percent?

Future value = $10 ×(1 + .051)(2065-1949) = $3,205.64

Your parents spent $7,800 to buy 200 shares of stock in a new company 12 years ago. The stock has appreciated 14.6 percent per year on average. What is the current value of those 200 shares?

Future value = $7,800 ×(1 + .146)12 = $40,023.03

Kendall is investing $3,333 today at 3 percent annual interest for three years. Which one of the following will increase the future value of that amount?

Increasing the interest rate

Ben invested $7,500 twenty years ago with an insurance company that has paid him 6 percent simple interest on his funds. Charles invested $7,500 twenty years ago in a fund that has paid him 6 percent interest, compounded annually. How much more interest has Charles earned than Ben over the past 20 years?

Interest on interest = $7,500 ×(1 + .06)20- [$7,500 + ($7,500 ×.06 ×20)] = $7,553.52

A preferred stock pays an annual dividend of $4.50. What is one share of this stock worth to you today if you require a rate of return of 11 percent?

P = $4.50/.11 = $40.91

Imprudential, Inc., has an unfunded pension liability of $763 million that must be paid in 15 years. To assess the value of the firm's stock, financial analysts want to discount this liability back to the present. If the relevant discount rate is 7 percent, what is the present value of this liability?

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Solve for the unknown interest rate in each of the following:

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ST Trucking just signed a $3.8 million contract. The contract calls for a payment of $1.1 million today, $1.3 million one year from today, and $1.4 million two years from today. What is this contract worth today at a discount rate of 8.7 percent?

PV = $1.1m + ($1.3m/1.087) + ($1.4m/1.0872) = $3,480,817.37

Assume a project will produce cash flows of $22,400, $28,700, $30,300, $10,900 at the end of Years 1 to 4, respectively. If the discount rate is 14.7 percent, what is the current value of these cash flows?

PV = $22,400 / 1.147 + $28,700 / 1.1472 + $30,300 / 1.1473 + $10,900 / 1.1474 = $67,721.24

Assume you pay $24,000 today in exchange for an annuity with monthly payments, an APR of 6.75 percent, and a life of 15 years.What is the payment amount?

PV = $24,000 = C ×[(1 - {1 / [1 + (.0675 / 12)]180}) / (.0675 / .12)] C = $212.38

Good Guys will pay you $2,500 a year for 10 years in exchange for $31,300 today. What interest rate will you earn on this annuity?

PV = $31,300 = $2,500 × {1 - [1 / (1 + r)10]} / r r = 3.89 percent

Which one of the following is the correct formula for the current value of $600 invested today at 5 percent interest for 6 years?

PV = $600 / (1 + .05)6

An investment will pay you $98,000 in three years. Assume the appropriate discount rate is 8 percent compounded daily. What is the present value?

PV = $98,000 / [(1 + .0800 / 365)3(365)] PV = $77,091.56

Eulis Co. has identified an investment project with the following cash flows.

PV@10% = $1,270 / 1.10 + $1,210 / 1.102 + $1,580 / 1.103 + $1,940 / 1.104 = $4,666.67 PV@18% = $1,270 / 1.18 + $1,210 / 1.182 + $1,580 / 1.183 + $1,940 / 1.184 = $3,907.54 PV@24% = $1,270 / 1.24 + $1,210 / 1.242 + $1,580 / 1.243 + $1,940 / 1.244 = $3,460.39

An investment will pay you $92,000 in six years. Assume the appropriate discount rate is 6.5 percent compounded daily. What is the present value?

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Assume that in 2014, an 1870 $20 double eagle sold for $16,800. What was the rate of return on this investment?

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Eulis Co. has identified an investment project with the following cash flows.

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For each of the following annuities, calculate the annual cash flow

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For each of the following annuities, calculate the present value.

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You want to buy a new sports coupe for $74,300, and the finance office at the dealership has quoted you a loan with an APR of 6.7 percent for 72 months to buy the car. What will your monthly payments be? What is the effective annual rate on this loan?

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You want to have $35,000 in cash to buy a car 3 years from today. You expect to earn 3.6 percent, compounded annually, on your savings. How much do you need to deposit today if this is the only money you save for this purpose?

Present value = $35,000/(1 + .036)3= $31,476.67

You want to have $40,000 for a down payment on a house 4 years from now. If you can earn 5.6 percent, compounded annually on your savings, how much do you need to deposit today to reach your goal?

Present value = $40,000/(1 + .056)4 = $32,166.54

When you were born, your parents opened an investment account in your name and deposited $1,500 into the account. The account has earned an average annual rate of return of 5.3percent. Today, the account is valued at $42,856. How old are you?

$42,856 = $1,500 ×(1 + .053)t t = 64.91 years

You want to invest an amount of money today and receive back twice that amount in the future. You expect to earn 6 percent interest. Approximately how long must you wait for your investment to double in value?

12 years

At 5 percent interest, how long does it take to double your money?

14.21

At 5 percent interest, how long does it take to quadruple your money?

28.41

You have been told that you need $25,600 today in order to have $100,000 when you retire 35 years from now. What rate of interest was used in the present value computation? Assume interest is compounded annually.

3.97

Imprudential, Inc., has an unfunded pension liability of $761 million that must be paid in 30 years. To assess the value of the firm's stock, financial analysts want to discount this liability back to the present. If the relevant discount rate is 9 percent, what is the present value of this liability?

57,357,434.59

Which one of the following has the highest effective annual rate?

6 percent compounded daily

Jenny needs to borrow $5,500 for four years. The loan will be repaid in one lump sum at the end of the loan term. Which one of the following interest rates is best for Jenny?

6.5 percent simple interest

You're trying to save to buy a new car valued at $48,690. You have $38,000 today that can be invested at your bank. The bank pays 3.7 percent annual interest on its accounts. How long will it be before you have enough to buy the car for cash? Assume the price of the car remains constant.

6.82 years

n 1893, the first Green Jacket Golf Championship was held. The winner's prize money was $230. In 2015, the winner's check was $1,570,000.What was the annual percentage increase in the winner's check over this period? If the winner's prize increases at the same rate, what will it be in 2043?

7.5 $ 11,908,951.09

In 1893, the first Green Jacket Golf Championship was held. The winner's prize money was $230. In 2015, the winner's check was $1,570,000. What was the annual percentage increase in the winner's check over this period? f the winner's prize increases at the same rate, what will it be in 2043?

7.50 ± 1% 11,908,951.10 ± .01%

Lisa has $1,000 in cash today. Which one of the following investment options is most apt to double her money?

8 percent interest for 9 years

Which one of the following will increase the present value of a lump sum future amount to be received in 15 years?

A decrease in the interest rate

All else held constant, the future value of a lump sum investment will decrease if the:

interest rate increases.

The relationship between the present value and the number of periods is best described as:

inverse

Jeff deposits $3,000 into an account which pays 2.5 percent interest, compounded annually. At the same time, Kurt deposits $3,000 into an account paying 5 percent interest, compounded annually. At the end of three years:

kurt will have a larger account value

Find the APR, or stated rate, in each of the following cases.

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For each of the following annuities, calculate the annual cash flow

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Sue needs to invest $3,626 today in order for her savings account to be worth $5,000 six years from now. Which one of the following terms refers to the $3,626?

present value

n 1897, the first Green Jacket Golf Championship was held. The winner's prize money was $170. In 2015, the winner's check was $1,510,000. What was the annual percentage increase in the winner's check over this period? If the winner's prize increases at the same rate, what will it be in 2043?

r = (FV / PV)1/t - 1 r = ($1,510,000 / $170)1/118 - 1 r = .0801, or 8.01% FV = PV(1 + r)t FV = $1,510,000(1.0801)28 FV = $13,059,176.78

Assume that in 2014, an 1876 $20 double eagle sold for $16,400. What was the rate of return on this investment?

r = (FV / PV)1/t - 1 r = ($16,400 / $20)1/138 - 1 r = .0498, or 4.98%

Although appealing to more refined tastes, art as a collectible has not always performed so profitably. Assume that in 2015, an auction house sold a statute at auction for a price of $10,563,500. Unfortunately for the previous owner, he had purchased it in 2011 at a price of $12,605,500. What was his annual rate of return on this sculpture?

-4.32 ± 1% Pic taken

How long will it take to double your savings if you earn 6.4 percent interest, compounded annually?

11.17 years $2 = $1 ×(1 + .064)t

Imprudential, Inc., has an unfunded pension liability of $765 million that must be paid in 25 years. To assess the value of the firm's stock, financial analysts want to discount this liability back to the present. If the relevant discount rate is 8 percent, what is the present value of this liability?

111,703,697.26 ± 0.01% Pic taken

Your aunt loaned you money at 1.00 percent interest per month. What is the APR of this loan?

APR = 1.00 ×12 = 12 percent

Katie's Dinor spent $113,800 to refurbish its current facility. The firm borrowed 65 percent of the refurbishment cost at 6.82 percent interest for six years. What is the amount of each monthly payment?

Amount borrowed = .65 ×$113,800 = $73,970 PV = $73,970 = C × (1 - {1 / [1 + (.0682 / 12)]72}) / (.0682 / 12) C = $1,254.73

Which one of the following qualifies as an annuity payment?

Auto loan payment

You and your sister are planning a large anniversary party 3 years from today for your parents' 50th wedding anniversary. You have estimated that you will need $6,500 for this party. You can earn 2.6 percent compounded annually on your savings. How much would you and your sister have to deposit today in one lump sum to pay for the entire party?

Present value = $6,500/(1 + .026)3 = $6,018.26

The future value of a lump sum investment will increase if you:

increase the time period.

Christie is buying a new car today and is paying a $500 cash down payment. She will finance the balance at 6.3 percent interest. Her loan requires 36 equal monthly payments of $450 each with the first payment due 30 days from today. Which one of the following statements is correct concerning this purchase?

To compute the initial loan amount, you must use a monthly interest rate.

Lucas expects to receive a sales bonus of $7,500 one year from now. The process of determining how much that bonus is worth today is called:

discounting.

Anna pays .85 percent interest monthly on her credit card account. When the interest rate on that debt is expressed as if it were compounded annually, the rate would be referred to as the:

effective annual rate.

Assume all else is equal. When comparing savings accounts, you should select the account that has the:

highest effective annual rate.

The stated interest rate is the interest rate expressed:

in terms of the interest payment made each period.