Suppose you are going to receive $11.0 per year for five years. The appropriate
ID: 2790155 • Letter: S
Question
Suppose you are going to receive $11.0 per year for five years. The appropriate interest rate is 9 percent. a. What is the present value of the payments if they are in the form of an ordinary annuity? (Do not round Intermediate calculations a Present value What is the present value of the payments if the payments are an annuity due? (Do not round Intermediate calculations and round Present value $ b. Suppose you plan to invest the payments for five years. What is the future value if the payments are an ordinary annuity? (Do not ro e.g., 32.16.) Future valueS What is the future valuelr the payments are an annuity due? (Do not round intermediate calculations and round your answer to 2d Future value
Explanation / Answer
a.
Formula for present value of ordinary annuity:
PV = P x [1 – (1 + r)-n/r]
Where,
PV = Present value of ordinary annuity
P = Payment per period = $ 11,000
r = rate per period = 9 % = 0.09
n = no. of periods = 5
PV = $ 11,000 x [1-(1+0.09)-5/0.09]
= $ 11,000 x [1-(1.09)-5/0.09]
= $ 11,000 x [1-0.649931386/0.09]
= $ 11,000 x [0.350068614/0.09]
= $ 11,000 x 3.889651263
= $ 42,786.16
Formula for present value of annuity due:
PV = P + P x [1 – (1 + r)-(n-1)/r]
Where,
PV = Present value of annuity due
P = Payment per period = $ 11,000
r = rate per period = 9 % = 0.09
n = no. of periods = 5
PV = $ 11,000 + $ 11,000 x [1-(1+0.09)(-5-1)/0.09]
= $ 11,000 + $ 11,000 x [1-(1.09)-4/0.09]
= $ 11,000 + $ 11,000 x [1-0.708425211/0.09]
= $ 11,000 + $ 11,000 x [0.291574789/0.09]
= $ 11,000 + $ 11,000 x 0.291574789
= $ 11,000 + $ 35,636.91865
= $ 46,636.92
b.
Formula for future value of ordinary annuity:
FV = P x [(1+r)n -1/r]
Where,
FV = Future value of ordinary annuity
P = Payment per period = $ 11,000
r = rate per period = 9 % = 0.09
n = no. of periods = 5
FV = $ 11,000 x [(1+0.09)5-1/0.09]
= $ 11,000 x [(1.09)5-1/0.09]
= $ 11,000 x (1.538623955-1/0.09)
= $ 11,000 x (0.538623955/0.09)
= $ 11,000 x 5.98471061
= $ 65,831.82
Formula for future value of annuity due:
FV = P x [(1+r)n -1/r](1+r)
Where,
FV = Future value of annuity due
P = Payment per period = $ 11,000
r = rate per period = 9 % = 0.09
n = no. of periods = 5
FV = $ 11,000 x [(1+0.09)5-1/0.09](1+0.09)
= $ 11,000 x [(1.09)5-1/0.09](1.09)
= $ 11,000 x (1.538623955-1/0.09)(1.09)
= $ 11,000 x (0.538623955/0.09)(1.09)
= $ 11,000 x 5.98471061 x 1.09
= $ 71,756.68
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