Question

____​20.​What is the PV of an ordinary annuity with 10 payments of $2,700 if the appropriate interest rate is 6.5%?

a.

$15,809.44

b.

$16,641.51

c.

$17,517.38

d.

$18,439.35

e.

$19,409.84

____​21.​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

e.

$939,459.18

____​22.​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

e.

$25,126.31

____​23.​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

____​24.​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.

$8,508.74

b.

$8,956.56

c.

$9,427.96

d.

$9,924.17

e.

$10,446.50

____​25.​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

____​26.​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

____​27.​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

e.

27.35

____​28.​You just won the state 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 one year from today. What rate of return is built into the annuity?

a.

6.72%

b.

7.07%

c.

7.43%

d.

7.80%

e.

8.19%

____​29.​Assume that you own an annuity that will pay you $15,000 per year for 12 years, with the first payment being made today. 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%

____​30.​What's the present value of a perpetuity that pays $250 per year if the appropriate interest rate is 5%?

a.

$4,750.00

b.

$5,000.00

c.

$5,250.00

d.

$5,512.50

e.

$5,788.13

Answer 1

Question Summary :

Different situations on calculation of Present and future values is given.

Solution:

A1) ​ PV of an ordinary annuity with 10 payments of $2,700 if the appropriate interest rate is 6.5%?

Answer option e : $19,409.84

Formula

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

= $2,000 × ( 1 −1 / (1+0.065)^ 10 ​)​ / 0.065

=19409.84

A2) PV of future annuity for 25 years at 6.25 % of $65000

Answer option b : $811,540.16

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

= $65,000 × ( 1 −1 / (1+0.0625)^ 25 ​)​ / 0.0625

= $811,540.16

A3) the PV of an annuity due with 10 payments of $2,700 at an interest rate of 6.5%

Answer option a   $20,671.48

Formula  

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

= 2700/0.065 * ( 1 −1 / (1+0.065)^ 10​)​ (1 +0.065)

= 20671.48

A4) Present value of annuity that pays $550 at the beginning of each year for 3 years at 5.5%

Answer option c $1,565.48

Formula  

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

= 550/0.055 * ( 1 −1 / (1+0.055)^ 3​)​ (1 +0.055)

= 1565.48