Marian Kirk wishes to select the better of two 9-year annuities, C and D. Annuit
ID: 2786767 • Letter: M
Question
Marian Kirk wishes to select the better of two
9-year
annuities, C and D. Annuity C is an ordinary annuity of
$2 ,090
per year for
9
years. Annuity D is an annuity due of
1,810
per year for
9
years.
a.Find the future value of both annuities at the end of year
9,
assuming that Marian can earn (1)
12%
annual interest and (2)
24%
annual interest.
b.Use your findings in part a to indicate which annuity has the greater future value at the end of year
9
for both the (1)
12%
and (2)
24%
interest rates..
c.Find the present value of both annuities, assuming that Marian can earn (1)
12%
annual interest and (2)
24%
annual interest.
d.Use your findings in part c to indicate which annuity has the greater present value for both the (1)
12%
and (2)
24%
interest rates.
e. Briefly compare, contrast, and explain any differences between your findings using the
1212%
and
24%
interest rates in parts b and
d.
a.The future value of Annuity C at
1212%
interest is
$nothing .
(Round to the nearest cent.)The future value of Annuity D at
1212%
interest is
$nothing .
(Round to the nearest cent.)The future value of Annuity C at
2424%
interest is
$nothing .
(Round to the nearest cent.)The future value of Annuity D at
2424%
interest is
$nothing .
(Round to the nearest cent.)b.Using your findings in part
a,
which annuity has the greater future value at the end of year
99
at
1212%
interest? (Select the best answer below.)
Annuity Upper DAnnuity D
Annuity Upper CAnnuity C
Using your findings in part
a,
which annuity has the greater future value at the end of year
99
at
2424%
interest? (Select the best answer below.)
A.
Annuity Upper CAnnuity C
B.
Annuity Upper DAnnuity D
c.The present value of Annuity C at
1212%
interest is
$nothing .
(Round to the nearest cent.)The present value of Annuity D at
1212%
interest is
$nothing .
(Round to the nearest cent.)The present value of Annuity C at
2424%
interest is
$nothing .
(Round to the nearest cent.)The present value of Annuity D at
2424%
interest is
$nothing .
(Round to the nearest cent.)d.Using your findings in part
c,
which annuity has the greater present value at the end of year
99
at
1212%
interest?(Select the best answer below.)
Annuity Upper DAnnuity D
Annuity Upper CAnnuity C
Using your findings in part
c,
which annuity has the greater present value at the end of year
99
at
2424%
interest?(Select the best answer below.)
A.
Annuity Upper CAnnuity C
B.
Annuity Upper DAnnuity D
e. Briefly compare, contrast, and explain any differences between your findings using the
1212%
and
2424%
interest rates in parts b and
d.
(Select the best answer from the drop-down menus.)Annuity C, with an annual payment of
2,090
made at the end of the year, has a
higher
lower
present value at
12%
than Annuity D with an annual payment of
1,810
made at the beginning of the year. When the rate is
decreased
increased
to
24%,
the shorter period of time to discount at the
higher
lower
rate results in a
larger
smaller
value for Annuity D, despite the
higher
lower
payment.
Explanation / Answer
a.
FV of ordinary annuity = P*[((1+r)^n - 1)/r]
FV of annuity due = P*[((1+r)^n - 1)/r] * (1+r)
P - Periodic payment
r - rate per period
n - number of periods
1. 12%
Option C
FV of ordinary annuity = 2090*[((1+0.12)^9 - 1)/0.12] = $30881.12
Option D
FV of annuity due = 1810*[((1+0.12)^9 - 1)/0.12] * (1+0.12) = $29953.21
2. 24%
Option C
FV of ordinary annuity = 2090*[((1+0.24)^9 - 1)/0.24] = $51649.02
Option D
FV of annuity due = 1810*[((1+0.24)^9 - 1)/0.24] * (1+0.24) = $55464.63
b.
When interest rate is 12%, option C has higher future value,
When interest rate is 24%, option D has higher future value.
c.
PV of ordinary annuity = P*[(1-(1+r)^(-n)) / r]
PV of annuity due = P*[(1-(1+r)^(-n)) / r] * (1+r)
P - Periodic payment
r - rate per period
n - number of periods
1. 12%
Option C
PV of ordinary annuity = 2090*[(1-(1+0.12)^(-9)) / 0.12] = 11136.04
Option C
PV of annuity due = 1810*[(1-(1+0.12)^(-9)) / 0.12] * (1+0.12) = 10801.43
2. 24%
Option C
PV of ordinary annuity = 2090*[(1-(1+0.24)^(-9)) / 0.24] = 7451.90
Option C
PV of annuity due = 1810*[(1-(1+0.12)^(-9)) / 0.12] * (1+0.12) = 8002.41
d.
When interest rate is 12%, option C has higher Present value
When interest rate is 24%, option D has higher present value.