Question

Jeff and John shared equally in an inheritance. Using his inheritance, John immediately bought a 10-year annuity-due with annual payments of 2500 each Jeff put his inheritance in an investment fund earning an annual effective interest rate of 9%. Two years later, Jeff bought a 15-year annuity-immediate with annual payment of Z. The present value of both annuities was determined using an annual effective interest rate of 8% Calculate Z. [SOA I1/96 84]

(A) 2330
(B) 2470
(C) 2515
(D) 2565 2715

Answer 1

(A) 2330

Step-by-step explanation:

The present value of John's annuity = $2,500 x 7.24689 (PVIFAnnuity due, 8%, 10 periods) = $18,117.23

Jeff deposited $18,117.23 x 1.09 = $19,747.78

The annual dsitribution = $19,747.78 / 8.55948 (PVIFA, 8%, 15 periods) = $2,307.12

Since I used annuity factors, the answer is only an approximation. The closest option is (A)