Question 1

What annual rate of return would Jia need to earn if she deposits $20,000 per year into an account beginning one year from today in order to have a total of $1,000,000 in 30 years?

Accepted Answer

To find the annual rate of return Jia needs to earn, we can use the future value formula:

FV = PMT x (1 + r)^n - 1 / r

where: 
FV = Future Value = $1,000,000 
PMT = Annual deposit = $20,000 
r = Annual rate of return we are trying to find 
n = Number of years = 30

Plugging in the values, we get:

$1,000,000 = $20,000 x (1 + r)^30 - 1 / r

Solving for r using trial and error or a financial calculator, we get r ≈ 3.3%. Therefore, the best choice is B.

Question 2

Ten years ago, Tom purchased a painting for $300. The painting is now worth $1,020. Tom could have deposited $300 in a savings account paying 12 percent interest compounded annually. Which of these two options would have provided Tom with a higher return?

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Question 3

The following table presents the Sally's Silly Service Company's net earnings for the past six years. Compute the growth rate in the company's earnings.

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The answer of The following table presents the Sally's Silly...

Question 4

Danny Joe borrows $10,500 from the bank at 11 percent annually compounded interest to be repaid in six equal annual installments. The interest paid in the first year is

Accepted Answer

The interest paid in the first year is calculated on the initial loan amount. Since the interest rate is 11 percent annually, the interest for the first year is 11% of $10,500, which is $1,155.

Question 5

How long would it take for Nico to save an adequate amount for retirement if he deposits $40,000 per year into an account beginning one year from today that pays 12 percent per year if he wishes to have a total of $1,000,000 at retirement?

Accepted Answer

The future value of an annuity is given by the formula:FV = P * [(1 + r)^n - 1] / rwhere:P is the annual paymentr is the annual interest raten is the number of yearsIn this case, we have:P = $40,000r = 12%FV = $1,000,000Solving for n, we get:n = log[(FV * r) / (P + FV * r)] / log(1 + r)= log[(1,000,000 * 0.12) / (40,000 + 1,000,000 * 0.12)] / log(1 + 0.12)= 15.0 yearsTherefore, it will take Nico 15 years to save an adequate amount for retirement.

Question 6

How long would it take for you to save an adequate amount for retirement if you deposit $40,000 per year into an account beginning today that pays 12 percent per year if you wish to have a total of $1,000,000 at retirement?

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The answer of How long would it take for you...

Question 7

Entertainer's Aid plans five annual colossal concerts, each in a different nation's capital. The concerts will raise funds for an endowment which would provide the World Wide Hunger Fund with $3,000,000 per year into perpetuity. The endowment will be given at the end of the fifth year. The rate of interest is expected to be 9 percent in all future periods. How much must Entertainer's Aid deposit each year to accumulate to the required amount?

Accepted Answer

The present value of the endowment is $3,000,000 / 0.09 = $33,333,333. The present value of the five deposits is $33,333,333 / (1 + 0.09)^5 = $18,302,746. The annual deposit is $18,302,746 / 5 = $3,660,549.

Question 8

Janice borrows $25,000 from the bank at 15 percent to be repaid in 10 equal annual installments. Calculate the end-of-year payment.

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The answer of Janice borrows $25,000 from the bank at...

Question 9

You have been given the opportunity to earn $20,000 five years from now if you invest $9,524 today. What will be the rate of return to your investment?

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The answer of You have been given the opportunity to...

Question 10

A firm wishes to establish a fund which, in 10 years, will accumulate to $10,000,000. The fund will be used to repay an outstanding bond issue. The firm plans to make deposits, which will earn 12 percent, to this fund at the end of each of the 10 years prior to maturity of the bond. How large must these deposits be to accumulate to $10,000,000?

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Question 11

Aunt Butch borrows $19,500 from the bank at 8 percent annually compounded interest to be repaid in 10 equal annual installments. The interest paid in the third year is ________.

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The answer of Aunt Butch borrows $19,500 from the bank...

Question 12

Find the equal annual end-of-year payment on $50,000, 15 year, and 10 percent loan.

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Question 13

A wealthy art collector has decided to endow her favorite art museum by establishing funds for an endowment which would provide the museum with $1,000,000 per year for acquisitions into perpetuity. The art collector will give the endowment upon her fiftieth birthday 10 years from today. She plans to accumulate the endowment by making annual end-of-year deposits into an account. The rate of interest is expected to be 6 percent in all future periods. How much must the art collector deposit each year to accumulate to the required amount?

Accepted Answer

To find out how much the art collector must deposit each year to accumulate to the required amount, we can use the formula for the future value of an annuity:

FV = PMT × ((1 + r)n - 1) / r

where FV is the future value of the annuity, PMT is the annual deposit, r is the interest rate, and n is the number of years.

In this case, we want the future value to be $1,000,000 per year, the interest rate is 6%, and the number of years is 10 (since the art collector will start making deposits in 10 years and wants to accumulate the required amount by then).

So we have:

$1,000,000 = PMT × ((1 + 0.06)^10 - 1) / 0.06

Solving for PMT, we get:

PMT = $1,000,000 × 0.06 / ((1 + 0.06)^10 - 1) = $1264445.93

Rounding to the nearest dollar, the answer is (C) $1,264,446.

Question 14

The New York Soccer Association would like to accumulate $10,000 by the end of 4 years from now to finance a big soccer weekend for its members. The Association currently has $2,500 and wishes to raise the balance by arranging annual fund-raising events. How much money should they raise at each annual fund-raising event assuming 8 percent rate of interest?

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The answer of The New York Soccer Association would like...

Question 15

Rita borrows $4,500 from the bank at 9 percent annually compounded interest to be repaid in three equal annual installments. The interest paid in the third year is ________.

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The answer of Rita borrows $4,500 from the bank at...

Question 16

How many years would it take for Jughead to save an adequate amount for retirement if he deposits $2,000 per month into an account beginning today that pays 12 percent per year if he wishes to have a total of $1,000,000 at retirement?

Accepted Answer

We can use the formula for future value of an annuity to solve this problem:

FV = PMT x (((1 + r)^n - 1) / r)

Where:
PMT = $2,000 (monthly deposit)
r = 12%/12 = 1% (monthly interest rate)
n = number of months

We want to find n, so we can rearrange the formula as follows:

n = ln(FV x r / PMT + 1) / ln(1 + r)

Plugging in the values, we get:

n = ln($1,000,000 x 0.01 / $2,000 + 1) / ln(1.01)
n ≈ 178.93 months

To convert months to years, we divide by 12:

n ≈ 14.91 years

Therefore, it would take Jughead about 14.9 years to save an adequate amount for retirement if he deposits $2,000 per month into an account beginning today that pays 12 percent per year if he wishes to have a total of $1,000,000 at retirement.

Question 17

Marc has purchased a new car for $15,000. He paid $2,500 as down payment and he paid the balance by a loan from his hometown bank. The loan is to be paid on a monthly basis for two years charging 12 percent interest. How much are the monthly payments?

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Question 18

What effective annual rate of return (EAR) would Rayne need to earn if she deposits $1,000 per month into an account beginning one month from today in order to have a total of $1,000,000 in 30 years?

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Question 19

John borrowed $12,000 to buy a new car and expects to pay $564.87 per month for the next 2 years to pay off the loan. What is the loan's rate of interest?

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The answer of John borrowed $12,000 to buy a new...

Question 20

What annual rate of return would Grandma Zoe need to earn if she deposits $1,000 per month into an account beginning one month from today in order to have a total of $1,000,000 in 30 years?

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The answer of What annual rate of return would Grandma...

Quiz 5: Time Value of Money