Question

Jane receives a 10-year increasing annuity-immediate paying 100 the first year and increasing by 100 each year thereafter. Mary receives a 10-year decreasing annuity-immediate paying X the first year and decreasing by X/10 each year thereafter. At an effective annual interest rate of 5%, both annuities have the same present value. Calculate X.

a. 860
b. 864
c. 868
d. 872
e. 876

Answer 1

b. 864

Step-by-step explanation:

Jane; Pv = P.a 10? + Q[(a.10? - 10v^10)/i}]

Pv = 100(7.7217) + 100[(7.7217 - 6.1391)/0.05]

Pv = 3937.38

Mary; Pv = P.a 10? + Q[(a.10? - 10v^10)/i}]

Pv = x(7.7217) - (x/10)[(7.7217 - 6.1391)/0.05]

Pv = 7.7217x - (x/10)(31.6521) = 4.5565x

Equating Pv for both Jane and Mary

3937.38 = 4.5565x

x = 3937.38/4.5565 = 864.124

x = 864.124 = 864