BCOR 340: principles of finance; homework 2

You have $300 today and want to triple your money in 5 years. What interest rate must you earn if the interest is compounded annually?

24.57 percent Explanation: $900 = $300 × (1 + r)^5 r = 24.57 %

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.

Rob wants to invest $15,000 for 7 years. Which one of the following rates will provide him with the largest future value? - 3 percent simple interest - 3 percent interest, compounded annually - 2 percent interest, compounded annually - 4 percent simple interest - 4 percent interest, compounded annually

4 percent interest, compounded annually

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 Explanation: Future value- 35 years = $5,000 × (1 + .05)^35 = $27,580.08 Future value- 30 years = $5,000 × (1 + .05)^30 = $21,609.71

Today, Georgia is investing $24,000 at 5.5 percent, compounded annually, for 6 years. How much additional income could she earn if she had invested this amount at 6.5 percent, compounded annually?

$1,927.19 Explanation: Difference $35,019.42 − 33,092.23 = $1,927.19

You want to have $32,000 for a down payment on a house 5 years from now. If you can earn 4.3 percent, compounded annually on your savings, how much do you need to deposit today to reach your goal?

$25,925.58 Explanation: Present value = $32,000/(1 + .043)^5 = $25,925.58

What is the future value of $8,000 invested today and held for 15 years at 8.5 percent compounded annually?

$27,197.94 Explanation: Future value = $8,000 × (1.085)^15 = $27,197.94

Theodoro has just received an insurance settlement of $18,500. She wants to save this money until her daughter goes to college. If she can earn an average of 5.2 percent, compounded annually, how much will she have saved when her daughter enters college 9 years from now?

$29,195.33 Explanation: Future value = $18,500 × (1 + .052)^9 = $29,195.33

Twelve years from now, you will be inheriting $60,000 What is this inheritance worth to you today if you can earn 6.0 percent interest, compounded annually?

$29,818.16 Explanation: Present value = $60,000/(1 + .06)^12 = $29,818.16

You deposit $1,675 into an account that earns 2.35 percent interest in two years. If you deposit an additional $1,950 in the same account 2 years later, how much would be in the account six years from now?

$3,880.81 Explanation: FV = 1,838.09 + FV = 2,042.73 = 3,880.81

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 Explanation: Future value = $5,500 × (1 + .092)^13 × (1 + .06)(25−13) = $34,747.80

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?

$7,553.52 Explanation: Interest on interest = $7,500 ×(1 + .06)^20 − [$7,500 + ($7,500 × .06 × 20)] = $7,553.52

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.

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

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

11.53 years Explanation: $3 = $1 × (1 + .10)^t t = 11.53 years

You just won $17,500 and deposited your winnings into an account that pays 6.7 percent interest, compounded annually. How long will you have to wait until your winnings are worth $50,000?

16.19 years

You have been told that you need $15,000 today for every $50,000 you want when you retire 30 years from now. What rate of interest was used in the present value computation? Assume interest is compounded annually.

4.09 percent Explanation: $50,000 = $15,000 × (1 + r)^30 r = 4.09 %

You want to invest an amount of money today and receive back twice that amount in the future. You expect to earn 9 percent interest. Approximately how long must you wait for your investment to double in value?

8 years Explanation: Approximate time period = 72/9 = 8 years

Which statement is true? - All else equal, an ordinary annuity is more valuable than an annuity due. - All else equal, a decrease in the number of payments increases the future value of an annuity due. - An annuity with payments at the beginning of each period is called an ordinary annuity. - All else equal, an increase in the discount rate decreases the present value and increases the future value of an annuity. - All else equal, an increase in the number of annuity payments decreases the present value and increases the future value of an annuity.

All else equal, an increase in the discount rate decreases the present value and increases the future value of an annuity.

Which one of the following statements concerning annuities is correct? - The present value of an annuity is equal to the cash flow amount divided by the discount rate. - An annuity due has payments that occur at the beginning of each time period. - The future value of an annuity decreases as the interest rate increases. - If unspecified, you should assume an annuity is an annuity due. - An annuity is an unending stream of equal payments occurring at equal intervals of time.

An annuity due has payments that occur at the beginning of each time period.

Travis is buying a car and will finance it with a loan that requires monthly payments of $265 for the next four years. His car payments can be described by which one of the following terms? - Perpetuity - Annuity - Consol - Lump sum - Present value

Annuity

Janis just won a scholarship that will pay her $500 a month, starting today, and continuing for the next 48 months. Which one of the following terms best describes these scholarship payments? - Ordinary annuity - Annuity due - Consol - Ordinary perpetuity - Perpetuity due

Annuity due

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

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

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 + .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

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 + .07)^6

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 - Compound value - Future value - Complex value - Factor value

Present value

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 will earn the same amount of interest each year. - She could have the same future value and invest less than $2,000 initially if she could earn more than 6.5 percent interest. - She will earn an increasing amount of interest each and every year even if she should decide to withdraw the interest annually rather than reinvesting the interest. - Her interest for Year 2 will be equal to $2,000 × .065 × 2. - She will be earning simple interest.

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. Explanation: 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

Which one of the following features distinguishes an ordinary annuity from an annuity due? - Number of equal payments - Amount of each payment - Frequency of the payments - Annuity interest rate - Timing of the annuity payments

Timing of the annuity payments

Which one of these is a perpetuity? - Trust income of $1,200 a year forever - Retirement pay of $2,200 a month for 20 years - Lottery winnings of $1,000 a month for life - Car payment of $260 a month for 60 months - Rental payment of $800 a month for one year

Trust income of $1,200 a year forever

The Jones Brothers recently established a trust fund that will provide annual scholarships of $12,000 indefinitely. These annual scholarships are:

a perpetuity.

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

compounding.

All else held constant, the present value of an annuity will decrease if you:

decrease the annuity payment.

Perpetuities have:

equal payments and an infinite life.

All else held constant, the future value of an annuity will increase if you:

increase the time period.

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.