(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
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