Q36: Megan purchases a perpetuity-immediate for 3250 with annual payments of 130. At the same price...
Q36:
Megan purchases a perpetuity-immediate for 3250 with annual payments of 130. At the same price and interest rate, Chris purchases an annuity-immediate with 20 annual payments that begin at amount P and increase by 15 (growth) each year thereafter. Calculate P .
Correct answer is: 116
Homework Answers
Present value of perpetuity = Annual payment / Interest
rate
3250 = 130 / Interest rate
Interest rate = 130 / 3250 = 0.04 or 4%
r = 0.04
n = 20
D = 15
(1/r) * (1 - (1 / (1 + r)^n)) = (1/0.04) * (1 -
(1/(1+0.04)^20))
= 25 * (1 - 0.4564)
= 13.5903
PV = 3250 = (P * 13.5903) + (15 * (13.5903 - 20/(1 + 0.04)^20) /
0.04
3250 = (P * 13.5903) + (15 * (13.5903 - 9.1277) / 0.04
3250 = (P * 13.5903) + (15 * (4.4626 / 0.04)
3250 = (P * 13.5903) + 1673.4750
P = (3250 - 1673.4750) / 13.5903
P = 1576.5250 / 13.5903
P = 116
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Q36:
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