An investment requires 10 equal annual payments, starting today, and will pay outalump sum of $500,000 15 years from today. lf the interest rate is 4% peryearcompounded annually, the required annual payment is closest to:
A $32.913.
B $34,230.
C $40,044.
答案是A
A. Correct because the present value of the future lump sum payment is PV = FV(1 + r)N= $500,000(1 + 0.04)-15 = $277,632.25. The 10 annual payments form an annuity due (since thepayments start today) whose present value equals the present value of an ordinary annuity with 9annual payments plus the first payment, i.e.PV= A + A[1- 1/(1 + r)N/r= A(1 + [1- 1/(1 +0.04)9/0.04)= 8.4353(A). Setting the PV of the cash outflows (the annuity) equal to the PV of thecash inflows (the return in 15 years), we can solve for the annual payment amount; A =$277,632.25/8.4353 ≈$32,913.Calculator solution: BGN; N = 10; I/Y = 4; PV = 277,632.25; solve forPMT = 32,913.
是不是还和先付年金和后付年金有关系呀，有点记不清了
