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(Related to Checkpoint 6.2) (Present value of an ordinary annuity)Nicki Johnson,

ID: 2809299 • Letter: #

Question

(Related to Checkpoint 6.2) (Present value of an ordinary annuity)Nicki Johnson, a sophomore mechanical engineering student, receives a call from an insurance agent who believes that Nicki is an older woman who is ready to retire from teaching. He talks to her about several annuities that she could buy that would guarantee her a fixed annual income. The annuities are as follows:

Annuity

Purchase Price of the

Annuity (At t = 0)

Amount of Money

Received Per Year

Duration of the

Annuity (Years)

A

$40,000

$7,500

12

B

$70,000

$9,000

22

C

$50,000

$6,000

20

Nicki could earn

9

percent on her money by placing it in a savings account. Alternatively, she could place it in any of the above annuities. Which annuities in the table above, if any, will earn Nicki a higher return than investing in the savings account earning

9

percent?

a.If Nicki could earn

9

percent on her money, what is the present value of annuity A with

$7,500

payments per year and

12

years duration?

Annuity

Purchase Price of the

Annuity (At t = 0)

Amount of Money

Received Per Year

Duration of the

Annuity (Years)

A

$40,000

$7,500

12

B

$70,000

$9,000

22

C

$50,000

$6,000

20

Explanation / Answer

a. Use rate function in Excel

PV = -40,000, PMT = 7500, N = 12, FV = 0

rate of return for A = 15.38%

similarly rate of return for B = 11.74%

rate of return for C = 10.32%

all three have rate of return more than 9%

b.

FV = 0, N =12, PMT = 7500, rate = 9%, use PV function in Excel

present worth of A = 53,705.44