Chapter 4 Finance Test

You have $5,000 you want to invest for the next 45 years. You are offered an investment plan that will pay you 6 percent per year for the next 15 years and 10 percent per year for the last 30 years. How much will you have at the end of the 45 years?

$209,092.54

What is the future value of $5,700 invested for 18 years at 9 percent compounded annually?

$26,887.59

You have just made your first $5,000 contribution to your retirement account. Assuming you earn a rate of return of 5 percent and make no additional contributions, what will your account be worth when you retire in 35 years? What if you wait for 5 years before contributing?

$27,580.08; 21,609.71

Stephen claims that he invested $6,000 six years ago and that this investment is worth $28,700 today. For this to be true, what annual rate of return did he have to earn? Assume the interest compounded annually.

$28,700 = $6,000 ×(1 + r)^6 r = 29.80 percent

Angela has just received an insurance settlement of $22,500. She wants to save this money until her daughter goes to college. If she can earn an average of 4.7 percent, compounded annually, how much will she have saved when her daughter enters college 6 years from now?

$29,638.94

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

$3 = $1 ×(1 + .10)t t = 11.53 years

Travis invests $5,500 today into a retirement account. He expects to earn 9.2 percent, compounded annually, on his money for the next 13 years. After that, he wants to be more conservative, so only expects to earn 6 percent, compounded annually. How much money will he have in his account when he retires 25 years from now, assuming this is the only deposit he makes into the account?

$34,747.80

You have $1,500 today in your savings account. How long must you wait for your savings to be worth $4,000 if you are earning 1.1 percent interest, compounded annually?

$4,000 = $1,500 ×(1 + 0.011)^t t = 89.66years

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?

$40,023.03

Marcos is investing $5 today at 7 percent interest so he can have $35 later. This $35 is referred to as the:

Future value

Today, Stacy is investing $18,000 at 6.72 percent, compounded annually, for 5 years. How much additional income could she earn if she had invested this amount at 7.15 percent, compounded annually?

Future value 6.72% = $18,000 × (1 + .0672)5 = $24,917.33 Future value 7.15% = $18,000 × (1 + .0715)5 = $25,423.39 Difference = $25,423.39- 24,917.33 = $506.06

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 grandparents just gave you a gift of $6,500. You are investing this money for 6 years at 4 percent simple interest. How much money will you have at the end of the 6 years?

Future value = $6,500 + ($6,500 ×.04 ×6) = $8,060

Today, you deposit $2,500 in a bank account that pays 3.6 percent simple interest. How much interest will you earn over the next 5 years?

Interest = $2,500 ×.036 ×5 = $450

Precision Engineering invested $125,000 at 6 percent interest, compounded annually for 3 years. How much interest on interest did the company earn over this period of time?

Interest on interest = $125,000 ×(1 + .06)^3- [$125,000 + ($125,000 ×.06 ×3)] = $1,377

Kevin just deposited $13,000 into his savings account at Traditions Bank. The bank will pay .87 percent interest, compounded annually, on this account. How much interest on interest will he earn over the next 5 years?

Interest on interest = $13,000 ×(1 + .0087)5- [$13,000 + ($13,000 ×.0087 ×5)] = $9.93

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

Stacey deposits $5,000 into an account that pays 2 percent interest, compounded annually. At the same time, Kurt deposits $5,000 into an account paying 3.5 percent interest, compounded annually. At the end of three years:

Kurt will have a larger account value than Stacey will

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

Which one of the following is the correct formula for computing the present value of $600 to be received in 6 years? The discount rate is 7 percent.

PV = $600/(1 + 0.07)6

Eight years from now, you will be inheriting $100,000. What is this inheritance worth to you today if you can earn 7.25 percent interest, compounded annually?

Present value = $100,000/(1 + .0725)^8 = $57,124.39

Starlite Industries will need $2.2 million 4.5 years from now to replace some equipment. Currently, the firm has some extra cash and would like to establish a savings account for this purpose. The account pays 3.6 percent interest, compounded annually. How much money must the company deposit today to fully fund the equipment purchase?

Present value = $2,200,000/(1 + .036)4.5= $1,876,306.49

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

Western Bank pays 5 percent simple interest on its savings account balances, whereas Eastern Bank pays 5 percent compounded annually. If you deposited $6,000in each bank, how much more money would you earn from the Eastern Bank account at the end of 3 years?

$45.75

Assume the total cost of a college education will be $325,000 when your child enters college in 16 years. You presently have $40,000 to invest and do not plan to invest anything further. What annual rate of interest must you earn on your investment to cover the entire cost of your child's college education?

13.99%

You have $500 today and want to triple your money in 6 years. What interest rate must you earn if the interest is compounded annually?

20.09%

You just won $30,000 and deposited your winnings into an account that pays 3.9 percent interest, compounded annually. How long will you have to wait until your winnings are worth $75,000?

23.95 years

You expect to receive $5,000 at graduation one year from now. Your plan is to invest this money at 6.5 percent, compounded annually, until you have $50,000. At that time, you plan to travel around the world. How long from now will it be until you can begin your travels?

37.57years

Rob wants to invest $15,000 for 7 years. Which one of the following rates will provide him with the largest future value?

4 percent interest, compounded annually

Suppose that in 2015, a $10 silver certificate from 1898 sold for $11,700. For this to have been true, what would the annual increase in the value of the certificate have been?

6.22 percent

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

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

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

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

interest is changed to simple interest from compound interest.

Jamie earned $14 in interest on her savings account last year. She has decided to leave the $14 in her account so that she can earn interest on the $14 this year. The interest earned on last year's interest earnings is called:

interest on interest

The relationship between the present value and the investment time period is best described as:

inverse

By definition, a bank that pays simple interest on a savings account will pay interest:

only on the principal amount originally invested.

Katlyn needs to invest $5,318 today in order for her savings account to be worth $8,000 six years from now. Which one of the following terms refers to the $5,318?

present value

Given an interest rate of zero percent, the future value of a lump sum invested today will always:

remain constant, regardless of the investment time period

Isaac only has $1,090 today but needs $1,979 to buy a new computer. How long will he have to wait to buy the computer if he earns 5.4 percent compounded annually on his savings? Assume the price of the computer remains constant.

$1,979 = $1,090 ×(1 + .054)^t t = 11.34 years

You are scheduled to receive $7,500 in two years. When you receive it, you will invest it at 4.5 percent per year. How much will your investment be worth ten years from now?

$10,665.75

You have been told that you need $32,000 today for each $100,000 you want when you retire 28 years from now. What rate of interest was used in the present value computation? Assume interest is compounded annually.

$100,000 = $32,000 ×(1 + r)^28 r = 4.15 percent

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

$2 = $1 ×(1 + .064)t t = 11.17 years

Eleven years ago, you deposited $3,200 into an account. Seven years ago, you added an additional $1,000 to this account. You earned 9.2 percent, compounded annually, for the first 4 years and 5.5 percent, compounded annually, for the last 7 years. How much money do you have in your account today?

$8,073.91

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

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

increase the time period

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

Jessica invested $2,000 today in an investment that pays 6.5 percent annual interest. Which one of the following statements is correct, assuming all interest is reinvested?

She could have the same future value and invest less than $2,000 initially if she could earn more than 6.5 percent interest

Sixty years ago, your grandparents opened two savings accounts and deposited $250 in each account. The first account was with City Bank at 3.6 percent, compounded annually. The second account was with Country Bank at 3.65 percent, compounded annually. Which one of the following statements is true concerning these accounts? (Do not round intermediate calculations.)

The Country Bank account has paid $61.30 more in interest than the City Bank account.

Which one of the following is a correct statement, all else held constant?

The future value is directly related to the interest rate.

Lester had $6,270 in his savings account at the beginning of this year. This amount includes both the $6,000 he originally invested at the beginning of last year plus the $270 he earned in interest last year. This year, Lester earned a total of $282.15 in interest even though the interest rate on the account remained constant. This $282.15 is best described as:

compound interest

Tomas earned $89 in interest on his savings account last year and has decided to leave the $86 in his account this coming year so it will earn interest. This process of earning interest on prior interest earnings is called:

compounding

The interest rate used to compute the present value of a future cash flow is called the:

discount rate

Computing the present value of a future cash flow to determine what that cash flow is worth today is called:

discounted cash flow valuation

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

The present value of a lump sum future amount:

increases as the interest rate decreases

Lew has $3,600 that he wants to invest for 5 years. He can invest this amount at his credit union and earn 2.2 percent simple interest. Or, he can open an account at Compass Bank and earn 2.15 percent interest, compounded annually. If he decides to invest at Compass Bank for 5 years, he will:

earn $8 more than if he had invested with his credit union.

Today, Charity wants to invest less than $3,000 with the goal of receiving $3,000 back some time in the future. Which one of the following statements is correct?

the period of time she has to wait decreases as the amount she invests increases

South Central Bank pays 2.5 percent interest, compounded annually, on its savings accounts. Northern Bank pays 2.5 percent simple interest on its savings accounts. You want to deposit sufficient funds today so that you will have $1,500 in your account 2 years from today. The amount you must deposit today:

will be greater if you invest with Northern Bank