BCOR 340 Homework 2

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.

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

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

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.

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 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

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 (1+r)^t= y Then original Multiplied by y

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?

$450.00

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?

$57,124.39

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?

$6,018.26

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

11.53 years

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 percent

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.

29.80 percent

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

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

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?

64.91 years

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?

89.66 years

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: A. aggregating. B. discounting. C. simplifying. D. compounding. E. extrapolating.

B.

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?

B. $506.06 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

Lisa has $1,000 in cash today. Which one of the following investment options is most apt to double her money? A. 6 percent interest for 3 years B. 12 percent interest for 5 years C. 7 percent interest for 9 years D. 8 percent interest for 9 years E. 6 percent interest for 10 years

D.

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: A. Both Stacey and Kurt will have accounts of equal value. B. Kurt will have twice the money saved that Stacey does. C. Kurt will earn exactly twice the amount of interest that Stacey earns. D. Kurt will have a larger account value than Stacey will. E. Stacey will have more money saved than Kurt.

D.

Which one of the following will increase the present value of a lump sum future amount to be received in 15 years? A. An increase in the time period B. An increase in the interest rate C. A decrease in the future value D. A decrease in the interest rate E. Changing to compound interest from simple interest

D.

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? A. $26,335.37; $23,011.60 B. $27,311.20; $29,803.04 C. $27,311.20; $22,614.08 D. $27,580.08; $21,609.71 E. $31,241.90; $32,614.08

D.

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? A. The period of time she has to wait until she reaches her goal is unaffected by the compounding of interest. B. The lower the rate of interest she earns, the shorter the time she will have to wait to reach her goal. C. She will have to wait longer if she earns 6 percent compound interest instead of 6 percent simple interest. D. The length of time she has to wait to reach her goal is not related to the interest rate she earns. E. The period of time she has to wait for decreases as the amount she invests increases.

E.

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

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?

Future value = $22,500 ×(1 + .047)6 = $29,638.94

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

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? Shortening the investment time period

Increasing the interest rate

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 + .06) ×5] PV = $600/ [(1 +.05) ×6] PV = $600/ (.06 ×5) PV = $600 / (1 + .05)6 PV = $600 / (1 + .06)5

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

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.) A. The City Bank account is currently worth $2,076.42. B. The City Bank account has paid $48.19 more in interest than the Country Bank account. C. The Country Bank account is currently worth $2,170.32. D. The Country Bank account has paid $72.24 more in interest than the City Bank account. E. The Country Bank account has paid $61.30 more in interest than the City Bank account.

The Country Bank account has paid $61.30 more in interest than the City Bank account. Future value City Bank = $250 ×(1 + .036)60 = $2,087.01 Future value Country Bank = $250 × (1 + .0365)60 = $2,148.32 Difference = $250 × [(1 + .0365)60-(1 + .036)60] = $61.30

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

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

discount rate.

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

discounted cash flow valuation.

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.

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

increase the time period.

The present value of a lump sum future amount: increases as the interest rate decreases. decreases as the time period decreases. is inversely related to the future value. is directly related to the interest rate. is directly related to the time period.

increases as the interest rate decreases.

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.