Question 1

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. How many years will it take to exhaust his funds, i.e., run the account down to zero?
A) 22.50
B) 23.63
C) 24.81
D) 26.05
E) 27.35

Accepted Answer

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

Question 2

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

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Question 3

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 determine the present value of the annuity, we use the formula:

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

where PV is the present value, PMT is the payment amount, r is the interest rate, and n is the total number of payments.

So, for the annuity, we have:

PV = $25,000 [((1 - (1 + 0.075)^-15) / 0.075)]
PV = $25,000 [((1 - 0.2233) / 0.075)]
PV = $25,000 (11.9746)
PV = $299,365.28

To determine the lump-sum, we need to find the present value of the annuity payments using the same interest rate of 7.5%.

So, we have:

PV = $25,000 [(1 - (1 + 0.075)^-15) / 0.075]
PV = $25,000 (11.9746)
PV = $299,365.28

Therefore, the lump sum must be equal to the present value of the annuity payments, which is $299,365.28.

Of the given answer choices, the closest value to this is B: $237,229.

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 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

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Question 6

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

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Question 7

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 formula for the present value of a perpetual annuity is A/i, where A is the annual payment and i is the interest rate. Plugging in the values, we get: 
Present Value = 250/0.05 = $5,000. Therefore, the answer is B.

Question 8

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, starting 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. For how many years can he make the $35,000 withdrawals and still have $25,000 left in the end?
A) 14.21
B) 14.96
C) 15.71
D) 16.49
E) 17.32

Accepted Answer

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Question 9

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

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Question 10

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 calculate the most you should pay for the annuity, you need to find the present value of the annuity payments using the formula:
PV = PMT x [(1 - (1 / (1 + r)^n)) / r], where PV is the present value, PMT is the payment amount, r is the discount rate (4.5% in this case), and n is the number of periods (5 years).
Plugging in the values, we get:
PV = $5,000 x [(1 - (1 / (1 + 0.045)^5)) / 0.045] = $21,938.07
Therefore, the most you should pay for the annuity is $21,938.07, which is closest to option C of $22,938.

Question 11

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 is a typical annuity problem where we have to find the amount of annuity payments that will allow the invested funds to be depleted in a specific time period. In this case, we need to find the amount of annuity payments that will allow the invested funds to be depleted in 25 years.

To solve the problem, we can use the formula for the present value of an annuity:

P = A x (1 - (1 + r)-n)/r

Where P is the present value of the annuity, A is the amount of each annuity payment, r is the annual interest rate, and n is the number of payments.

We know that the present value of the annuity is equal to the initial amount invested, which is $375,000. We also know the annual interest rate, which is 7.5%. Finally, we know the number of payments, which is 25.

So we can plug in these values and solve for the amount of each annuity payment:

375,000 = A x (1 - (1 + 0.075)-25)/0.075

375,000 = A x 11.798

A = 31,694.42

Therefore, the amount of each annuity payment should be approximately $31,294.42 to allow the invested funds to be depleted in 25 years. The best 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

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Question 13

Your Aunt Ruth 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. How many years will it take to exhaust her funds, i.e., run the account down to zero?
A) 18.62
B) 19.60
C) 20.63
D) 21.71
E) 22.86

Accepted Answer

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Question 14

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

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Question 15

Suppose you just won the state lottery, and you have a choice between receiving $2,550,000 today or a 20-year annuity of $250,000, with the first payment coming one year from today. What rate of return is built into the annuity? Disregard taxes.
A) 7.12%
B) 7.49%
C) 7.87%
D) 8.26%
E) 8.67%

Accepted Answer

To find the rate of return built into the annuity, we can use the present value formula for an annuity:

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

where PV = present value (in this case, $2,550,000), PMT = payment per year (in this case, $250,000), r = rate of return, and n = number of years (in this case, 20).

Substituting the values given, we get:

2,550,000 = 250,000 * ((1 - (1 + r)^-20) / r)

Solving for r using a financial calculator or spreadsheet program gives us 7.49%, which is option B.

Therefore, the best choice is to take the annuity, as it has a higher rate of return built into it than the lump sum payment.

Question 16

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 (PV) of the annuity, we can use the formula:

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

where PV is the present value, PMT is the payment per period (in this case, $550), r is the annual interest rate (5.5% or 0.055), and n is the number of periods (3).

Plug in the values and solve:

PV = $550 x (1 - 1/(1 + 0.055)^3)/0.055
PV = $1,565.48

Therefore, the most you should pay for the annuity is $1,565.48. Choice C is the closest option.

Question 17

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

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Question 18

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

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Question 19

Your aunt has $500,000 invested at 5.5%, and she now wants to retire. She wants to withdraw $45,000 at the beginning of each year, beginning immediately. She also wants to have $50,000 left to give you when she ceases to withdraw funds from the account. For how many years can she make the $45,000 withdrawals and still have $50,000 left in the end?
A) 15.54
B) 16.36
C) 17.22
D) 18.08
E) 18.99

Accepted Answer

To find out how many years your aunt can withdraw $45,000 and still have $50,000 left, we need to use the present value of an annuity formula:
PV = (PMT/i) x [1 - 1/(1+i)^n]
where PV is the present value (aka the initial investment), PMT is the withdrawal amount, i is the interest rate, and n is the number of years.

We know that PV = $500,000, PMT = $45,000, and i = 5.5%. We need to solve for n.

$500,000 = ($45,000/0.055) x [1 - 1/(1+0.055)^n]

Simplifying the right side of the equation:
$500,000 = $818,181.82 x [1 - 1/(1.055)^n]

Dividing both sides by $818,181.82:
0.611 = [1 - 1/(1.055)^n]

Subtracting 1 from both sides:
-0.389 = -1/(1.055)^n

Multiplying both sides by (1.055)^n:
(1.055)^n x -0.389 = -1

Dividing both sides by -0.389:
(1.055)^n = 2.568

Taking the natural log of both sides:
n x ln(1.055) = ln(2.568)

Dividing both sides by ln(1.055):
n = ln(2.568) / ln(1.055)

n ≈ 17.22

Therefore, your aunt can withdraw $45,000 for 17.22 years and still have $50,000 left at the end. The answer is C.

Question 20

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

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Quiz 5: Time Value of Money

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?

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 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?

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?

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

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%?

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?

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?

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?

Your Aunt Ruth 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. How many years will it take to exhaust her funds, i.e., run the account down to zero?

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

Suppose you just won the state lottery, and you have a choice between receiving $2,550,000 today or a 20-year annuity of $250,000, with the first payment coming one year from today. What rate of return is built into the annuity? Disregard taxes.

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?

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

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?

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?