An investor has $25,000 that he can invest today. In addition to this amount,he can also invest $12,000 per year for 30 years (beginning one year from now)at which time he will retire. He plans on living for 25 years after he retires. If interest rates are 8 percent,what size annual annuity payment can he obtain for his retirement years? (All annuity payments are at year-end. Round your answer to the nearest dollar.)

Question

Quizplus · Accepted Answer

To solve this problem, we need to use the future value of an annuity formula.

1. First, we will calculate the future value of the investor's investments from now until one year before retirement:

FV = $25,000 x (1 + 0.08)^30 + $12,000 x [(1 + 0.08)^30 - 1] / 0.08 
FV = $1,390,535

2. Next, we will calculate the size of the annuity payment that the investor can obtain for his retirement years:

PV = $1,390,535 
N = 25 (the number of years he will live after retiring) 
I/Y = 8% 
PMT = ? (the annuity payment we want to find)

Using a financial calculator or Excel, we can solve for PMT:

PMT = $150,913

Therefore, the annual annuity payment that the investor can obtain for his retirement years is $150,913, rounded to the nearest dollar.

The best choice is C.

An Investor Has $25,000 That He Can Invest Today