Answer to Question #129931 in Financial Math for Nahashon Kimathi

Question

John Carson is planning for his retirement. He is 45 year today and would like to have Sh.3, 000,000 when he attains the age of 60. He intends to deposit a constant amount at 12% each year in a pension fund to achieve his objective. How much should John invest at the end of each year, for the next 15 years to obtain Sh.3, 000,000 at the end of that period?

Answer 1

Let $X$ be a cash flow per year, $i=12\%=0.12$ be the interest rate, and $n=60-45=15$ be the number of payments.

Using formula $F_{ordinary\ annuity}=X\cdot[\frac{(1+i)^n-1}{i}]$ to calculate ordinary annuity $X$ , we have:

$3000000=X\cdot[\frac{(1+0.12)^{15}-1}{0.12}],\\ X=\frac{3000000}{[\frac{(1+0.12)^{15}-1}{0.12}]}\approx80472.72.$

Answer: $ 80472.72.