Question 1

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)$28,532.45
B)$29,959.08
C)$31,457.03
D)$33,029.88

Accepted Answer

The correct answer is A because the present value of the annuity is $275,000 and the interest rate is 8.25%. The number of periods is 20. The formula for the present value of an annuity is:PV = PMT * [1 - (1 + r)^-n] / rwhere:PV is the present valuePMT is the paymentr is the interest raten is the number of periodsSubstituting the given values into the formula, we get:$275,000 = PMT * [1 - (1 + 0.0825)^-20] / 0.0825PMT = $28,532.45Therefore, the amount that can be withdrawn at the end of each of the next 20 years is $28,532.45.

Question 2

What is the PV of an annuity due with 10 payments of $2,700 at an interest rate of 6.5%?
A)$20,671.48
B)$21,705.06
C)$22,790.31
D)$23,929.82

Accepted Answer

The present value of an annuity due is calculated as the present value of an ordinary annuity multiplied by (1 + r), where r is the interest rate. In this case, the present value of an ordinary annuity with 10 payments of $2,700 at an interest rate of 6.5% is $20,671.48. Multiplying this by (1 + 0.065) gives us $21,705.06, which is the present value of the annuity due.

Question 3

Your aunt is about to retire,and she wants to buy an annuity that will supplement her income by $65,000 per year for 25 years,beginning a year from today.The going rate on such annuities is 6.25%.How much would it cost her to buy such an annuity today?
A)$770,963.15
B)$811,540.16
C)$852,117.17
D)$894,723.02

Accepted Answer

To calculate the cost of the annuity, we can use the present value of an annuity formula:

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

Where:
PMT = $65,000
r = 6.25% = 0.0625 (annual interest rate)
n = 25 (number of years)

Plugging in the numbers, we get:

PV = 65,000 x [(1 - (1 / (1 + 0.0625)^25)) / 0.0625]
PV = $811,540.16

Therefore, it would cost your aunt $811,540.16 to buy the annuity today. Option B is correct.

Question 4

Your friend just won the lottery.She has the choice of $15,000,000 today or a 20-year annuity of $1,050,000,with the first payment coming 1 year from today.What rate of return is built into the annuity?
A)2.79%
B)3.10%
C)3.44%
D)3.79%

Accepted Answer

The rate of return built into the annuity can be found by calculating the internal rate of return (IRR) for the cash flows. The IRR is the rate at which the present value of the annuity payments equals the lump sum amount. In this case, the IRR is approximately 3.44%.

Question 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?
A)$28,243.21
B)$29,729.70
C)$31,294.42
D)$32,859.14

Accepted Answer

To find the annual withdrawal amount, we use the formula for the present value of an annuity. Solving for the withdrawal amount with the given interest rate and time period results in approximately $31,294.42.

Question 6

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

Accepted Answer

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

Question 7

What is the PV of an ordinary annuity with 10 payments of $2,700 if the appropriate interest rate is 6.5%?
A)$16,641.51
B)$17,517.38
C)$18,439.35
D)$19,409.84

Accepted Answer

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

Question 8

You want to go to Europe 5 years from now,and you can save $3,100 per year,beginning 1 year from today.You plan to deposit the funds in a mutual fund that you expect to return 8.5% per year.Under these conditions,how much will you have just after you make the fifth deposit,5 years from now?
A)$18,368.66
B)$19,287.09
C)$20,251.44
D)$21,264.02

Accepted Answer

The correct answer is A because the future value of the annuity can be calculated using the formula: FV = PMT * [(1 + r)^n - 1] / r, where PMT is the annual deposit, r is the annual interest rate, and n is the number of years. Plugging in the given values, we get: FV = 3100 * [(1 + 0.085)^5 - 1] / 0.085 = 18368.66.

Question 9

Your uncle has $375,000 and wants to retire.He expects to live for another 25 years and to be able 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

Accepted Answer

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

Question 10

You have a chance to buy an annuity that pays $1,200 at the end 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)$2,775.77
B)$2,921.86
C)$3,075.64
D)$3,237.52

Accepted Answer

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

Question 11

You want to buy a new sports car 3 years from now,and you plan to save $4,200 per year,beginning 1 year from today.You will deposit your savings in an account that pays 5.2% interest.How much will you have just after you make the third deposit,3 years from now?
A)$11,973.07
B)$12,603.23
C)$13,266.56
D)$13,929.88

Accepted Answer

We can use the formula for the future value of an annuity to find the amount we will have just after making the third deposit:

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

where:
PMT = annual deposit = $4,200
r = annual interest rate = 5.2% = 0.052
n = number of years = 3

Substituting these values, we get:

FV = 4,200 * ((1 + 0.052)^3 - 1) / 0.052
FV = $13,266.56

Therefore, the best choice is C.

Question 12

You want to buy a new sports car 3 years from now,and you plan to save $4,200 per year,beginning immediately.You will make three deposits in an account that pays 5.2% interest.Under these assumptions,how much will you have 3 years from today?
A)$13,956.42
B)$14,654.24
C)$15,386.95
D)$16,156.30

Accepted Answer

The correct answer is A because the future value of the three deposits can be calculated using the formula: FV = PV * (1 + r)^n, where PV is the present value, r is the annual interest rate, and n is the number of years. In this case, the present value is $4,200, the annual interest rate is 5.2%, and the number of years is 3. Plugging these values into the formula, we get: FV = $4,200 * (1 + 0.052)^3 = $13,956.42.

Question 13

Your uncle has $500,000 invested at 7.5%,and he now wants to retire.He wants to withdraw $40,000 at the beginning of each year,beginning immediately.How many years will it take to exhaust his funds,i.e.,run the account down to zero?
A)24.38
B)25.66
C)27.01
D)28.44

Accepted Answer

The answer of Your uncle has $500,000 invested at 7.5%,and...

Question 14

You want to go to Europe 5 years from now,and you can save $3,100 per year,beginning immediately.You plan to deposit the funds in a mutual fund that you expect to return 8.5% per year.Under these conditions,how much will you have just after you make the fifth deposit,5 years from now?
A)$17,986.82
B)$18,933.49
C)$19,929.99
D)$20,926.49

Accepted Answer

We can solve this problem using the Future Value formula for an annuity:

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

where:

Pmt = the annual deposit amount
r = the annual interest rate
n = the number of years
FV = the future value of the annuity

Plugging in the given values, we get:

Pmt = $3,100
r = 8.5% = 0.085
n = 5

FV = $3,100 x [(1+0.085)^5 - 1] / 0.085
FV = $19,929.99

Therefore, you will have $19,929.99 just after you make the fifth deposit, 5 years from now. The correct answer is choice (C).

Question 15

Your aunt is about to retire,and she wants to buy an annuity that will provide her with $65,000 of income a year for 25 years,with the first payment coming immediately.The going rate on such annuities is 6.25%.How much would it cost her to buy the annuity today?
A)$739,281.38
B)$778,190.93
C)$819,148.35
D)$862,261.42

Accepted Answer

The answer of Your aunt is about to retire,and she...

Question 16

You own an oil well that will pay you $30,000 per year for 10 years,with the first payment being made today.If you think a fair return on the well is 8.5%,how much should you ask for if you decide to sell it?
A)$202,893
B)$213,572
C)$224,250
D)$235,463

Accepted Answer

We can use the Present Value formula to calculate the fair price for the well:
PV = CF / (1 + r)^n
where PV is the present value, CF is the cash flow, r is the interest rate, and n is the number of periods.

In this case, CF = $30,000 per year for 10 years, r = 8.5%, and n = 10. The first payment is already made, so we need to calculate the present value of the remaining 9 payments:
PV = $30,000 {(1 - (1 + 0.085)^-9) / 0.085} = $213,572

Therefore, the fair price to sell the well would be $213,572. The closest answer choice is B.

Question 17

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

Accepted Answer

The most you should pay for the annuity is the present value of the annuity payments. Since the payments are made at the beginning of each year, it's an annuity due. The present value of an annuity due can be calculated using the formula: PV = PMT * [(1 - (1 + r)^-n) / r] * (1 + r), where PMT is the payment amount, r is the interest rate, and n is the number of periods. Plugging in the values: PV = $550 * [(1 - (1 + 0.055)^-3) / 0.055] * (1 + 0.055) = $1,565.48.

Question 18

Your uncle has $375,000 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.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

Accepted Answer

The answer of Your uncle has $375,000 invested at 7.5%,and...

Question 19

You just won the lottery,and you have a choice between receiving $3,500,000 today or a 10-year annuity of $500,000,with the first payment coming 1 year from today.What rate of return is built into the annuity?
A)6.72%
B)7.07%
C)7.43%
D)7.80%

Accepted Answer

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

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

where PV is the present value of the annuity ($3,500,000 in this case), PMT is the payment per period ($500,000), r is the rate of return per period, and n is the number of periods (10 years).

Plugging in the numbers and solving for r gives:

$3,500,000 = $500,000 * (1 - 1/(1+r)^10) / r

r = 7.07%

Therefore, the best choice is to take the annuity, as the rate of return (7.07%) is higher than what could be earned through a low-risk investment like a savings account.

Question 20

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)$8,956.56
B)$9,427.96
C)$9,924.17
D)$10,446.50

Accepted Answer

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

Quiz 4: Time Value of Money

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?

What is the PV of an annuity due with 10 payments of $2,700 at an interest rate of 6.5%?

Your aunt is about to retire,and she wants to buy an annuity that will supplement her income by $65,000 per year for 25 years,beginning a year from today.The going rate on such annuities is 6.25%.How much would it cost her to buy such an annuity today?

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

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?

What is the PV of an ordinary annuity with 10 payments of $2,700 if the appropriate interest rate is 6.5%?

You want to go to Europe 5 years from now,and you can save $3,100 per year,beginning 1 year from today.You plan to deposit the funds in a mutual fund that you expect to return 8.5% per year.Under these conditions,how much will you have just after you make the fifth deposit,5 years from now?

Your uncle has $375,000 and wants to retire.He expects to live for another 25 years and to be able 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?

You have a chance to buy an annuity that pays $1,200 at the end 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?

You want to buy a new sports car 3 years from now,and you plan to save $4,200 per year,beginning 1 year from today.You will deposit your savings in an account that pays 5.2% interest.How much will you have just after you make the third deposit,3 years from now?

You want to buy a new sports car 3 years from now,and you plan to save $4,200 per year,beginning immediately.You will make three deposits in an account that pays 5.2% interest.Under these assumptions,how much will you have 3 years from today?

Your uncle has $500,000 invested at 7.5%,and he now wants to retire.He wants to withdraw $40,000 at the beginning of each year,beginning immediately.How many years will it take to exhaust his funds,i.e.,run the account down to zero?

You want to go to Europe 5 years from now,and you can save $3,100 per year,beginning immediately.You plan to deposit the funds in a mutual fund that you expect to return 8.5% per year.Under these conditions,how much will you have just after you make the fifth deposit,5 years from now?

Your aunt is about to retire,and she wants to buy an annuity that will provide her with $65,000 of income a year for 25 years,with the first payment coming immediately.The going rate on such annuities is 6.25%.How much would it cost her to buy the annuity today?

You own an oil well that will pay you $30,000 per year for 10 years,with the first payment being made today.If you think a fair return on the well is 8.5%,how much should you ask for if you decide to sell it?

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 uncle has $375,000 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.How many years will it take to exhaust his funds,i.e.,run the account down to zero?

You just won the lottery,and you have a choice between receiving $3,500,000 today or a 10-year annuity of $500,000,with the first payment coming 1 year from today.What rate of return is built into the annuity?

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%?