Question 1

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

BEGIN Mode
      N                           5
$\begin{array}{lr}
\text { I/YR } & 5.5 \% \
\text { PMT } & \$ 2,500 \
\text { FV } & \$ 0.00 \
\text { PV } & \$ 11.262 .88
\end{array}$

Question 2

You were left $100,000 in a trust fund set up by your grandfather.The fund 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

BEGIN Mode
 $$\begin{array} { l r }
\text { N } & 4 \ 
\text { I/YR } & 6.5 \%\
\text { PV } &\$100,000  \
\text { FV } & \$0.00 \
\text { PMT } & \$27,409
\end{array}$$

Question 3

Your uncle just won the weekly lottery,receiving $375,000,which he invested at a 7.5% annual rate.He now has decided 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at the end of each year,starting at the end of this year.What is the maximum number of whole payments that can be withdrawn before the account is exhausted,i.e.,before the account balance would become negative?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

$$\begin{array} { l r } 
\text { I/YR } & 7.5 \% \
\text { PV } & - \$ 375,000 \
\text { PMT } & \$ 35,000 \
\text { FV } & 0.00 \
\mathrm {~N} & 22.50 \
\mathrm {~N} \text { rounded } & 22
\end{array}$$

Question 4

Now that your uncle has decided to retire,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

BEGIN Mode
       N                        25
$\begin{array}{lr}
\mathrm{I} / \mathrm{YR} & 5.15 \% \
\text { PMT } & \$ 85,000 \
\text { FV } & \$ 0.00 \
\text { PV } & \$ 1,240,960
\end{array}$

Question 5

After receiving a reward for information leading to the arrest of a notorious criminal,you are considering investing it in 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

N                     20
$\begin{array}{lr}
\text { I/YR } & 5.0 \% \
\text { PMT } & \$ 5,000 \
\text { FV } & \$ 0.00 \
\text { PV } & \$ 62,311
\end{array}$

Question 6

A perpetuity pays $85 per year and costs $950.What is the rate of return?
A) 8.95%
B) 9.39%
C) 9.86%
D) 10.36%
E) 10.88%

Accepted Answer

$\begin{array}{lr}
\text { Cost }(\mathrm{PV}) & \$ 950 \
\mathrm{PMT} & \$ 85 \
\mathrm{YPR} & 8.95 \%
\end{array}$

Question 7

Geraldine was injured in a car accident,and the insurance company has offered her 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 her 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

BEGIN Mode
       N                       15
$\begin{array}{lr}
\text { I/YR } & 7.5 \% \
\text { PMT } & \$ 25,000 \
\text { FV } & \$ 0.00 \
\text { PV } & \$ 237,229
\end{array}$

Question 8

Because your mother is about to retire,she wants to buy an annuity that will provide her 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 her to buy the annuity today?
A) $825,835
B) $869,300
C) $915,052
D) $963,213
E) $1,011,374

Accepted Answer

BEGIN Mode
      N                     20
$\begin{array}{lr}
\text { I/YR } & 5.25 \% \
\text { PMT } & \$ 75,000 \
\text { FV } & \$ 0.00 \
\text { PV } & \$ 963,213
\end{array}$

Question 9

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

$$\begin{array} { l r } 
\text { I/YR } & 7.50 \% \
\text { PV } & - \$ 300,000 \
\text { PMT } & \$ 35,000 \
\text { FV } & \$25,000 \
\mathrm {~N} & 13.48 \
\mathrm {~N} \text { rounded } & 13
\end{array}$$

Question 10

Your aunt wants to retire and has $375,000.She expects to live for another 25 years,and she also expects to earn 7.5% on her invested funds.How much could she 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

BEGIN Mode
 $$\begin{array} { l r } 
\text { N} & 25\
\text { I/YR } & 7.5 \%  \
\text { MV } &\$375,000 \
\text { FV } & \$0.00\
\text { PMT } & \$31,294.42
\end{array}$$

Question 11

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

BEGIN Mode
 $$\begin{array} { l r } 
\text { I/YR } & 6.5 \% \
\text { PV } & - \$ 500,000 \
\text { PMT } & \$40,000 \
\text { FV } &\$0.00 \
\mathrm {~N} & 22.86 \
\mathrm {~N} \text { rounded } & 22
\end{array}$$

Question 12

An uncle of yours who is about to retire wants to sell some of his stock and buy an annuity that will provide him 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 him to buy such an annuity today?
A) $574,924
B) $605,183
C) $635,442
D) $667,214
E) $700,575

Accepted Answer

N                     30
$\begin{array}{lr}
\mathrm{I} / \mathrm{YR} & 7.25 \% \
\text { PMT } & \$ 50,000 \
\mathrm{FV} & \$ 0.00 \
\mathrm{PV} & \$ 605.183
\end{array}$

Question 13

A new investment opportunity for you is 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

BEGIN Mode
      N                        3
$\begin{array}{lr}
\mathrm{I} / \mathrm{YR} & 5.5 \% \
\text { PMT } & \$ 550 \
\text { FV } & \$ 0.00 \
\text { PV } & \$ 1,565.48
\end{array}$

Question 14

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

BEGIN Mode
 $$\begin{array} { l r } 
\text { N } & 20 \
\text { I/YR } & 8.25 \% \
\text {PV } &\$ 275,000  \
\text { FV } & \$0.00\
\text { PMT } &\$26,357.92
\end{array}$$

Question 15

Your aunt wants to retire and has $375,000.She expects to live for another 25 years and to earn 7.5% on her invested funds.How much could she 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

$$\begin{array} { l r } 
\text { N } & 25 \
\text { I/YR } & 7.5 \% \
\text {PV } &  \$375,000 \
\text { FV } &\$0.00 \
\text { PMT } & \$33,641.50
\end{array}$$

Question 16

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

N                   4
$\begin{array}{lr}
\mathrm{I} / \mathrm{YR} & 5.0 \% \
\text { PMT } & \$ 2,250 \
\mathrm{FV} & \$ 3,000 \
\mathrm{PV} & \$ 10.446
\end{array}$
 
Alternative setup:
 11ea42d0_c06d_71cd_9abf_3b9861b77559_TB2090_00

Question 17

A salt mine you inherited 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 mine 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

BEGIN Mode
      N                          25
$\begin{array}{lr}
\text { I/YR } & 7.5 \% \
\text { PMT } & \$ 25,000 \
\text { FV } & \$ 0.00 \
\text { PV } & \$ 299,574
\end{array}$

Question 18

Your father is considering purchasing an annuity that pays $5,000 at the beginning of each year for 5 years.He could earn 4.5% on his money in other investments with equal risk.What is the most he should pay for the annuity?
A) 20,701
B) $21,791
C) $22,938
D) $24,085
E) $25,289

Accepted Answer

BEGIN Mode
     N                       5
$\begin{array}{lr}
\mathrm{IYR} & 4.5 \% \
\text { PMT } & \$ 5,000 \
\text { FV } & \$ 0.00 \
\text { PV } & \$ 22,938
\end{array}$

Question 19

Suppose you earned a $275,000 bonus this year 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

$$\begin{array} { l r } 
\text {N}&20\
\text { I/YR } & 8.25 \% \
\text { IV } &  \$275,000\
\text { FV } & \$0.00 \
\text { PMT } &\$28,532  \
\end{array}$$

Question 20

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

$$\begin{array} { l r } 
\text { I/YR } & 5 .0 \% \
\text { PMT } & \$ 250 \
\text { PV } &\$ 5,000
\end{array}$$

Quiz 4: Time Value of Money

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

Now that your uncle has decided to retire,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 perpetuity pays $85 per year and costs $950.What is the rate of return?

Geraldine was injured in a car accident,and the insurance company has offered her 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 her as well off financially as with the annuity?

Because your mother is about to retire,she wants to buy an annuity that will provide her 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 her to buy the annuity today?

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

An uncle of yours who is about to retire wants to sell some of his stock and buy an annuity that will provide him 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 him to buy such an annuity today?

A new investment opportunity for you is 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?

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 aunt wants to retire and has $375,000.She expects to live for another 25 years and to earn 7.5% on her invested funds.How much could she 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 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 salt mine you inherited 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 mine is 7.5%,how much should you ask for it if you decide to sell it?

Your father is considering purchasing an annuity that pays $5,000 at the beginning of each year for 5 years.He could earn 4.5% on his money in other investments with equal risk.What is the most he should pay for the annuity?

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

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