Question 1

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 2

What is the present value of the following cash flow stream at a rate of 12.0%? 
A) $9,699
B) $10,210
C) $10,747
D) $11,284
E) $11,849

Accepted Answer

The answer of What is the present value of the...

Question 3

Assume that you own an annuity that will pay you $15,000 per year for 12 years, with the first payment being made today. You need money today to start a new business, and your uncle offers to give you $120,000 for the annuity. If you sell it, what rate of return would your uncle earn on his investment? A) 6.85% B) 7.21% C) 7.59% D) 7.99% E) 8.41%

Accepted Answer

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Question 4

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 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? 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 6

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

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Question 7

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. What is the maximum number of $45,000 withdrawals that she can make and still have at least
$50,000 left in the account? (Hint: If your solution for N is not an integer, round down to the nearest whole number.)
A) 13
B) 14
C) 15
D) 16
E) 17

Accepted Answer

The maximum number of withdrawals is calculated using the formula for the present value of an annuity due. Solving for N, the number of withdrawals, gives approximately 15.

Question 8

What annual payment must you receive in order to earn a 6.5% rate of return on a perpetuity that has a cost of $1,250?
A) $77.19
B) $81.25
C) $85.31
D) $89.58
E) $94.06

Accepted Answer

The formula for calculating the annual payment on a perpetuity is: Payment = Cost of Perpetuity × Rate of Return

Plugging in the given values, we get:

Payment = $1,250 × 6.5% = $81.25

Therefore, the annual payment you must receive in order to earn a 6.5% rate of return on a perpetuity that has a cost of $1,250 is $81.25.

Question 9

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 out the rate of return built into the annuity, we need to use the present value formula:

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

where PV is the present value of the annuity, PMT is the annual payment, r is the annual interest rate, and n is the number of years.

If we set PV equal to the lump sum of $2,550,000, PMT equal to $250,000, and n equal to 20, we can solve for r:

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

Solving for r using a financial calculator or spreadsheet function yields approximately 7.49%.

Therefore, the best choice is to take the lump sum of $2,550,000 today. This option would provide more money upfront and could be invested to potentially earn a higher return than the 7.49% built into the annuity.

Question 10

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 11

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 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

To find the cost of the annuity, we need to calculate the present value of 25 years of $85,000 payments, using the given interest rate of 5.15%.

We can use the present value formula for an annuity:

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

where PV is the present value, PMT is the annuity payment, r is the interest rate, and n is the number of periods.

Plugging in the values we get:

PV = $85,000 x (1 - 1/(1+0.0515)^25) / 0.0515
PV = $1,240,960

Therefore, it would cost him $1,240,960 to buy the annuity today.

The correct answer is D.

Question 13

Your girlfriend just won the Florida lottery. She has the choice of
$15,000,000 today or a 20-year annuity of $1,050,000, with the first payment coming one year from today. What rate of return is built into the annuity?
A) 3.44%
B) 3.79%
C) 4.17%
D) 4.58%
E) 5.04%

Accepted Answer

To solve this problem, first we need to find the present value of the annuity using the formula: PV = PMT*((1- (1/(1+r)^n))/r), where PV is the present value, PMT is the annual payment, r is the annual interest rate, and n is the number of periods (years). Plugging in the given values, we get:

PV = $1,050,000*((1- (1/(1+r)^20))/r)

Next, we can use a financial calculator or trial and error to find the interest rate that makes the present value of the annuity equal to the $15,000,000 lump sum. The answer is approximately 3.44%. Therefore, your girlfriend should choose the lump sum of $15,000,000 today instead of the annuity.

Question 14

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 15

What is the present value of the following cash flow stream at a rate of 8.0%? 
A) $7,917
B) $8,333
C) $8,772
D) $9,233
E) $9,695

Accepted Answer

The answer of What is the present value of the...

Question 16

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 present value of an annuity due problem, where the present value is $375,000, the interest rate is 7.5%, and the number of periods is 25. Using the formula for present value of an annuity due, we have:

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

Solving for PMT, we get:

PMT = PV / (((1 - (1 + r)^(-n)) / r) x (1 + r))
PMT = $375,000 / (((1 - (1 + 0.075)^(-25)) / 0.075) x (1 + 0.075))
PMT = $31,294.42

Therefore, he 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.

Question 17

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 70) 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

The annuity is an annuity due, so you need to calculate the present value of an annuity due. The present value of an annuity due is calculated by multiplying the present value of an ordinary annuity by (1 + r). Using the formula for the present value of an ordinary annuity and adjusting for the annuity due, the correct amount is approximately $22,938.

Question 18

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

The answer of You have a chance to buy an...

Question 19

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 20

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.

Quiz 4: Time Value of Money

What is the present value of the following cash flow stream at a rate of 12.0%?

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?

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 annual payment must you receive in order to earn a 6.5% rate of return on a perpetuity that has a cost of $1,250?

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.

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?

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 girlfriend just won the Florida lottery. She has the choice of $15,000,000 today or a 20-year annuity of $1,050,000, with the first payment coming one year from today. What rate of return is built into the annuity?

What is the present value of the following cash flow stream at a rate of 8.0%?

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?

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 70) Investments with equal risk. What is the most you should pay for 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?

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