Question 1

James plans to fund his individual retirement account,beginning today,with 20 annual deposits of $2,000.If he can earn an annual compound rate of 8 percent on his deposits,the amount in the account 20 years from today will be ________.

Accepted Answer

Using the formula for the future value of an annuity, we can calculate:

FV = PMT * [(1 + r)^n - 1] / r

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

Plugging in the values given:

FV = $2,000 * [(1 + 0.08)^20 - 1] / 0.08 
FV ≈ $98,846

Therefore, the amount in the account 20 years from today will be approximately $98,846. Choice C is the correct answer.

Question 2

A generous benefactor to a local ballet plans to make a one-time endowment that would provide the ballet with $150,000 per year into perpetuity.The rate of interest is expected to be 5 percent for all future time periods.How large must the endowment be?

Accepted Answer

To find the size of the endowment needed to provide $150,000 per year into perpetuity at an interest rate of 5%, you use the formula for perpetuity: Endowment = Annual Payment / Interest Rate. Plugging in the numbers: Endowment = $150,000 / 0.05 = $3,000,000.

Question 3

Calculate the present value of an annuity of $3,900 each year for four years,assuming an opportunity cost of 10 percent.

Accepted Answer

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Question 4

Calculate the present value of a $10,000 perpetuity at a 6 percent discount rate.

Accepted Answer

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Question 5

A wealthy industrialist wishes to establish a $2,000,000 trust fund which will provide income for his grandchild into perpetuity.He stipulates in the trust agreement that the principal may not be distributed.The grandchild may only receive the interest earned.If the interest rate earned on the trust is expected to be at least 7 percent in all future periods,how much income will the grandchild receive each year?

Accepted Answer

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Question 6

Calculate the future value of an annuity of $5,000 each year for eight years,deposited at 6 percent.

Accepted Answer

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Question 7

The future value of an ordinary annuity of $2,000 each year for 10 years,deposited at 12 percent,is ________.

Accepted Answer

The future value of an ordinary annuity is the sum of the present values of each of the annuity payments. The present value of each payment is the payment amount divided by (1 + r)^n, where r is the interest rate and n is the number of years. In this case, the present value of each payment is $2,000 / (1 + 0.12)^10 = $1,130.00. The future value of the annuity is the sum of the present values of each of the payments, which is $1,130.00 * 10 = $11,300.00.

Question 8

Dottie has decided to set up an account that will pay her granddaughter $5,000 a year indefinitely.How much should Dottie deposit in an account paying 8 percent annual interest?

Accepted Answer

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Question 9

To pay for her college education,Gina is saving $2,000 at the beginning of each year for the next eight years in a bank account paying 12 percent interest.How much will Gina have in that account at the end of 8th year?

Accepted Answer

Gina is making a series of equal payments (an annuity) at the beginning of each year. The future value of an annuity due can be calculated using the formula: FV = P * [(1 + r)^n - 1] * (1 + r) / r, where P is the payment amount, r is the interest rate, and n is the number of periods. Plugging in the values: FV = $2,000 * [(1 + 0.12)^8 - 1] * (1 + 0.12) / 0.12, which results in approximately $27,551.

Question 10

The future value of a $10,000 annuity due deposited at 12 percent compounded annually for each of the next 5 years is ________.

Accepted Answer

An annuity due means payments are made at the beginning of each period. The future value of an annuity due can be calculated using the formula: FV = Pmt * [(1 + r)^n - 1] * (1 + r) / r. Plugging in the values: Pmt = $10,000, r = 0.12, n = 5, the future value is approximately $71,152.

Question 11

The present value of a perpetual income stream increases when the discount rate ________.

Accepted Answer

The present value of a perpetual income stream is calculated as the income divided by the discount rate. Therefore, as the discount rate decreases, the present value increases.

Question 12

You have been offered a project paying $300 at the beginning of each year for the next 20 years.What is the maximum amount of money you would invest in this project if you expect 9 percent rate of return to your investment?

Accepted Answer

To determine the maximum amount of money you should invest, you need to calculate the present value of the cash flows (payments) expected from the investment.

Using a financial calculator or a spreadsheet program, the present value of the annuity can be computed as:

PV = $300 × [(1 - 1/(1 + 0.09)^20) / 0.09]
PV = $300 × 12.5879
PV = $3,776.37

Therefore, the maximum amount you should invest is $2,985 (rounded to the nearest dollar), because investing more than that would result in a negative rate of return.

Question 13

A college received a contribution to its endowment fund of $2 million.It can never touch the principal,but can use the earnings.At an assumed interest rate of 9.5 percent,how much can the college earn to help its operations each year?

Accepted Answer

The college can use the earnings of the endowment fund, which is 9.5% of the principal. Therefore, the college can earn $190,000 each year (0.095 x $2,000,000 = $190,000). Hence, the correct answer is (C).

Question 14

A generous philanthropist plans to make a one-time endowment to a renowned heart research center which would provide the facility with $250,000 per year into perpetuity.The rate of interest is expected to be 8 percent for all future time periods.How large must the endowment be?

Accepted Answer

Using the perpetuity formula: PV = PMT/i, where PV is the present value, PMT is the annual payment, and i is the interest rate.
Plugging in the values: PV = $250,000/0.08 = $3,125,000

Question 15

The future value of a $2,000 annuity due deposited at 8 percent compounded annually for each of the next 10 years is ________.

Accepted Answer

Using the formula for future value of an annuity due, we get:

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

where PMT is the payment made at the beginning of each year, r is the interest rate, and n is the number of years.

Substituting the given values, we get:

FV = $2,000 x ((1 + 0.08)^(10+1) -1)/ 0.08
FV = $31,291

Therefore, the answer is B) $31,291.

Question 16

The future value of an ordinary annuity of $1,000 each year for 10 years,deposited at 3 percent,is ________.

Accepted Answer

We can use the formula for future value of an ordinary annuity:

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

where PMT is the annual payment, r is the interest rate, and n is the number of payments.

Plugging in the numbers, we get:

FV = 1,000 x [(1 + 0.03)^10 - 1] / 0.03
FV = $11,464.16

Therefore, the answer is B - $11,464.

Question 17

The present value of an ordinary annuity of $350 each year for five years,assuming an opportunity cost of 4 percent,is ________.

Accepted Answer

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Question 18

Rachel takes out a seven-year,8 percent loan with a bank requiring annual end-of-year payments of $960.43.Calculate the original principal amount.

Accepted Answer

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Question 19

The present value of an ordinary annuity of $2,350 each year for eight years,assuming an opportunity cost of 11 percent,is ________.

Accepted Answer