Question 1

What's the present value of a perpetuity that pays $250 per year if the appropriate interest rate is 5%?
A) $4,750
B) $5,000
C) $5,250
D) $5,513
E) $5,788

Accepted Answer

The present value formula for a perpetuity is PV = PMT / r, where PV is the present value, PMT is the annual payment, and r is the interest rate. Plugging in the values given in the question, we get PV = 250 / 0.05 = $5,000. Therefore, the present value of the perpetuity is $5,000, which is option B.

Question 2

Your uncle has $375,000 and wants to retire. He expects to live for another 25 years and to earn 7.5% on his invested funds. How much could he withdraw at the end of each of the next 25 years and end up with zero in the account?
A) $28,843.38
B) $30,361.46
C) $31,959.43
D) $33,641.50
E) $35,323.58

Accepted Answer

The answer of Your uncle has $375,000 and wants to...

Question 3

Suppose you inherited $275,000 and invested it at 8.25% per year. How much could you withdraw at the end of each of the next 20 years?
A) $28,532
B) $29,959
C) $31,457
D) $33,030
E) $34,681

Accepted Answer

The answer of Suppose you inherited $275,000 and invested it...

Question 4

Your grandmother just died and left you $100,000 in a trust fund that pays 6.5% interest. You must spend the money on your college education, and you must withdraw the money in 4 equal installments, beginning immediately. How much could you withdraw today and at the beginning of each of the next 3 years and end up with zero in the account?
A) $24,736
B) $26,038
C) $27,409
D) $28,779
E) $30,218

Accepted Answer

To find out the amount that can be withdrawn at the beginning of each year, we need to use the present value of an annuity formula.

The formula for calculating the present value of an annuity is:

PV = Pmt x (1 - (1 + r/n)^(-nt)) x (n/r)

Where: 
PV = present value 
Pmt = payment amount 
r = annual interest rate 
n = number of compound periods per year 
t = total number of years

In this case, we can calculate the payment amount (Pmt) as follows:

Pmt = PV / [(1 - (1 + r/n)^(-nt)) x (n/r)]

Where PV is the total amount in the trust fund, which is $100,000.

n = 1 (since it's compounded annually)
r = 0.065 (annual interest rate)
t = 4 (payment period)

Pmt = $27,409

Therefore, you can withdraw $27,409 at the beginning of each of the next 4 years (including today) to use up the entire trust fund and end up with zero in the account.

Option C is the correct answer.

Question 5

You have a chance to buy an annuity that pays $5,000 at the beginning of each year for 5 years. You could earn 4.5% on your money in other investments with equal risk. What is the most you should pay for the annuity? 
A) 20,701
B) $21,791
C) $22,938
D) $24,085
E) $25,289

Accepted Answer

To find the most you should pay for the annuity, we need to calculate the present value of the annuity using the formula:

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

where PV is the present value, PMT is the payment per period, r is the discount rate, and n is the number of periods.

In this case, PMT = $5,000, r = 4.5%, and n = 5. Plugging in these values, we get:

PV = $5,000 x [1 - (1 + 0.045)^(-5)]/0.045 = $22,938

Therefore, the most you should pay for the annuity is $22,938. The correct answer is C.

Question 6

You inherited an oil well that will pay you $25,000 per year for 25 years, with the first payment being made today. If you think a fair return on the well is 7.5%, how much should you ask for it if you decide to sell it?
A) $284,595
B) $299,574
C) $314,553
D) $330,281
E) $346,795

Accepted Answer

Using the perpetuity formula, we can calculate the present value of the oil well payments:

PV = PMT / r

where PV is the present value, PMT is the annual payment, and r is the required rate of return.

Plugging in the given values, we get:

PV = $25,000 / 0.075
PV = $333,333.33

Therefore, the oil well is currently worth $333,333.33. However, we need to discount this amount back to today's value since the first payment is being made today.

Using the present value of an annuity formula, we can calculate the present value of the 25-year annuity with a rate of 7.5%:

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

where PV is the present value, PMT is the annual payment, r is the required rate of return, and n is the number of periods.

Plugging in the given values, we get:

PV = $25,000 x [1 - (1 + 0.075)^-25] / 0.075
PV = $299,574.19

Therefore, if you decide to sell the oil well, you should ask for $299,574.19 to earn a fair rate of return of 7.5%. The answer is B.

Question 7

Your uncle has $300,000 invested at 7.5%, and he now wants to retire. He wants to withdraw $35,000 at the end of each year, beginning at the end of this year. He also wants to have $25,000 left to give you when he ceases to withdraw funds from the account. What is the maximum number of $35,000 withdrawals that he can make and still have at least $25,000 left in the account? (Hint: If your solution for N is not an integer, round down to the nearest whole number.)
A) 12
B) 13
C) 14
D) 15
E) 16

Accepted Answer

This problem can be solved using the formula for the present value of an annuity: $PV = PMT \times \left(\frac{1 - (1 + r)^{-n}}{r}\right)$, where PV is the present value (initial investment), PMT is the annual withdrawal amount, r is the annual interest rate, and n is the number of payments. Rearranging to solve for n, and considering the future value that needs to remain ($25,000), we adjust the equation to account for this by subtracting the future value discounted back to the present value from the initial investment. Using trial and error or financial calculators and plugging in the given values ($300,000 initial investment, 7.5% interest rate, $35,000 withdrawal), we find that the maximum number of $35,000 withdrawals that can be made while still leaving at least $25,000 in the account is 13.

Question 8

Suppose you inherited $275,000 and invested it at 8.25% per year. How much could you withdraw at the beginning of each of the next 20 years?
A) $22,598.63
B) $23,788.03
C) $25,040.03
D) $26,357.92
E) $27,675.82

Accepted Answer

The answer of Suppose you inherited $275,000 and invested it...

Question 9

You just inherited some money, and a broker offers to sell you an annuity that pays $5,000 at the end of each year for 20 years. You could earn 5% on your money in other investments with equal risk. What is the most you should pay for the annuity?
A) $50,753
B) $53,424
C) $56,236
D) $59,195
E) $62,311

Accepted Answer

The answer of You just inherited some money, and a...

Question 10

Sam was injured in an accident, and the insurance company has offered him the choice of $25,000 per year for 15 years, with the first payment being made today, or a lump sum. If a fair return is 7.5%, how large must the lump sum be to leave him as well off financially as with the annuity?
A) $225,367
B) $237,229
C) $249,090
D) $261,545
E) $274,622

Accepted Answer

To find the present value of the annuity, we use the formula: 
PMT * [(1 - (1 + r)^-n) / r]
where PMT = $25,000, r = 7.5%, and n = 15 years.

P = $25,000 * [(1 - (1 + 0.075)^-15)/0.075]
P = $25,000 * [(1 - 0.2562)/0.075]
P = $25,000 * 9.2158
P = $230,395

So, the lump sum should be equal to $230,395 to leave Sam as well off as the annuity.

To find the lump sum, we can use the formula for present value of a lump sum: 
PV = FV / (1 + r)^n
where FV is the desired lump sum, r = 7.5%, and n = 15 years.

PV = $25,000 * [(1 - (1 + 0.075)^-15)/0.075]
PV = $25,000 * 9.2158
PV = $230,395

So, the lump sum should be $230,395.

Among the given answer choices, we can see that the closest one is option B: $237,229. This makes it the best choice.

Question 11

You have a chance to buy an annuity that pays $550 at the beginning of each year for 3 years. You could earn 5.5% on your money in other investments with equal risk. What is the most you should pay for the annuity?
A) $1,412.84
B) $1,487.20
C) $1,565.48
D) $1,643.75
E) $1,725.94

Accepted Answer

To find the present value of the annuity, we can use the formula PV = PMT/((1+r)^n-1) * (1-1/(1+r)^n), where PV is the present value, PMT is the annual payment, r is the interest rate, and n is the number of years. Plugging in the values, we get PV = 550/((1+0.055)^3-1) * (1-1/(1+0.055)^3) = $1,565.48 (rounded to the nearest cent). Therefore, the most you should pay for the annuity is $1,565.48. The correct answer choice is C.

Question 12

Your father is about to retire, and he wants to buy an annuity that will provide him with $85,000 of income a year for 25 years, with the first payment coming immediately. The going rate on such annuities is 5.15%. How much would it cost him to buy the annuity today?
A) $1,063,968
B) $1,119,966
C) $1,178,912
D) $1,240,960
E) $1,303,008

Accepted Answer

The answer of Your father is about to retire, and...

Question 13

What's the rate of return you would earn if you paid $950 for a perpetuity that pays $85 per year?
A) 8.95%
B) 9.39%
C) 9.86%
D) 10.36%
E) 10.88%

Accepted Answer

The answer of What's the rate of return you would...

Question 14

Your aunt is about to retire, and she wants to sell some of her stock and buy an annuity that will provide her with income of $50,000 per year for 30 years, beginning a year from today. The going rate on such annuities is 7.25%. How much would it cost her to buy such an annuity today?
A) $574,924
B) $605,183
C) $635,442
D) $667,214
E) $700,575

Accepted Answer

The present value of an annuity formula is PV = PMT x ((1 - (1 / (1 + r)^n)) / r)
PV = $50,000 x ((1 - (1 / (1 + 0.0725)^30)) / 0.0725)
PV = $605,183. Therefore, the cost for the annuity is $605,183.

Question 15

What's the present value of a 4-year ordinary annuity of $2,250 per year plus an additional $3,000 at the end of Year 4 if the interest rate is 5%?
A) $8,509
B) $8,957
C) $9,428
D) $9,924
E) $10,446

Accepted Answer

The answer of What's the present value of a 4-year...

Question 16

Your uncle is about to retire, and he wants to buy an annuity that will provide him with $75,000 of income a year for 20 years, with the first payment coming immediately. The going rate on such annuities is 5.25%. How much would it cost him to buy the annuity today?
A) $825,835
B) $869,300
C) $915,052
D) $963,213
E) $1,011,374

Accepted Answer

The answer of Your uncle is about to retire, and...

Question 17

Your father's employer was just acquired, and he was given a severance payment of $375,000, which he invested at a 7.5% annual rate. He now plans to retire, and he wants to withdraw $35,000 at the end of each year, starting at the end of this year. What is the maximum number of whole payments that can be withdrawn before the account is exhausted; i.e., before the account balance would become negative? (Hint: Round down to the nearest whole number.)
A) 22
B) 23
C) 24
D) 25
E) 26

Accepted Answer

The answer of Your father's employer was just acquired, and...

Question 18

What is the PV of an annuity due with 5 payments of $2,500 at an interest rate of 5.5%?
A) $11,262.88
B) $11,826.02
C) $12,417.32
D) $13,038.19
E) $13,690.10

Accepted Answer

The answer of What is the PV of an annuity...

Question 19

Your Aunt Elsa has $500,000 invested at 6.5%, and she plans to retire. She wants to withdraw $40,000 at the beginning of each year, starting immediately. What is the maximum number of whole payments that can be withdrawn before the account is exhausted; i.e., before the account balance would become negative? (Hint: Round down to the nearest whole number.)
A) 18
B) 19
C) 20
D) 21
E) 22

Accepted Answer

The answer of Your Aunt Elsa has $500,000 invested at...

Question 20

Your uncle has $375,000 and wants to retire. He expects to live for another 25 years, and he also expects to earn 7.5% on his invested funds. How much could he withdraw at the beginning of each of the next 25 years and end up with zero in the account?
A) $28,243.21
B) $29,729.70
C) $31,294.42
D) $32,859.14
E) $34,502.10

Accepted Answer

This problem can be solved using the present value of an annuity formula. The formula is:

PMT = PV / ((1 - (1 + r)^(-n)) / r)

where PMT is the equal payment at the beginning of each year, PV is the present value of the funds, r is the interest rate, and n is the number of years.

Plugging in the given values, we get:

PMT = 375,000 / ((1 - (1 + 0.075)^(-25)) / 0.075)
PMT = $31,294.42 (rounded to the nearest cent)

Therefore, the uncle could withdraw $31,294.42 at the beginning of each of the next 25 years and end up with zero in the account. So the best choice is (C).

Quiz 4: Time Value of Money

What's the present value of a perpetuity that pays $250 per year if the appropriate interest rate is 5%?

Your uncle has $375,000 and wants to retire. He expects to live for another 25 years and to earn 7.5% on his invested funds. How much could he withdraw at the end of each of the next 25 years and end up with zero in the account?

Suppose you inherited $275,000 and invested it at 8.25% per year. How much could you withdraw at the end of each of the next 20 years?

You have a chance to buy an annuity that pays $5,000 at the beginning of each year for 5 years. You could earn 4.5% on your money in other investments with equal risk. What is the most you should pay for the annuity?

You inherited an oil well that will pay you $25,000 per year for 25 years, with the first payment being made today. If you think a fair return on the well is 7.5%, how much should you ask for it if you decide to sell it?

Suppose you inherited $275,000 and invested it at 8.25% per year. How much could you withdraw at the beginning of each of the next 20 years?

You just inherited some money, and a broker offers to sell you an annuity that pays $5,000 at the end of each year for 20 years. You could earn 5% on your money in other investments with equal risk. What is the most you should pay for the annuity?

Sam was injured in an accident, and the insurance company has offered him the choice of $25,000 per year for 15 years, with the first payment being made today, or a lump sum. If a fair return is 7.5%, how large must the lump sum be to leave him as well off financially as with the annuity?

You have a chance to buy an annuity that pays $550 at the beginning of each year for 3 years. You could earn 5.5% on your money in other investments with equal risk. What is the most you should pay for the annuity?

Your father is about to retire, and he wants to buy an annuity that will provide him with $85,000 of income a year for 25 years, with the first payment coming immediately. The going rate on such annuities is 5.15%. How much would it cost him to buy the annuity today?

What's the rate of return you would earn if you paid $950 for a perpetuity that pays $85 per year?

Your aunt is about to retire, and she wants to sell some of her stock and buy an annuity that will provide her with income of $50,000 per year for 30 years, beginning a year from today. The going rate on such annuities is 7.25%. How much would it cost her to buy such an annuity today?

What's the present value of a 4-year ordinary annuity of $2,250 per year plus an additional $3,000 at the end of Year 4 if the interest rate is 5%?

Your uncle is about to retire, and he wants to buy an annuity that will provide him with $75,000 of income a year for 20 years, with the first payment coming immediately. The going rate on such annuities is 5.25%. How much would it cost him to buy the annuity today?

What is the PV of an annuity due with 5 payments of $2,500 at an interest rate of 5.5%?

Your uncle has $375,000 and wants to retire. He expects to live for another 25 years, and he also expects to earn 7.5% on his invested funds. How much could he withdraw at the beginning of each of the next 25 years and end up with zero in the account?