Imagine that Homer Simpson actually invested $100 comma 000 5 years ago at a 7.5 percent annual interest rate. If he invested an additional $1 comma 500 a year at the beginning of each year for 20 years at the same 7.5 percent annual rate, how much money will Homer have 20 years from now

Total amount of money on both investments in 20 years will be $679,663

Explanation:

Firstly, we calculate the the return in the next 20 years expected on $100,000 , invested 5 years ago.

The mathematical formula to use is :

Future value = Present Value * (1 + interest rate)^number of years

The twist here is that the number of years is 25 and not 20 or 5. This is because he had invested 5 years ago and he’s expecting a return in the next 20 years. So total investment time would be 5 + 20 = 25 years

Future value = 100,000 * (1 + 7.5/100)^25

= 100,000 * (1+0.075)^25

= 100,000* (1.075)^25

= $609,834

Secondly, we now calculate the future value for an additional $1,500 per year for 20 years at same interest percentage

We use a mathematical approach to this also.

The formula to use is:

Future value = Annual payment * {[1+r]^n -1}/r * [1+r]

Where r is interest rate = 7.5/100 = 0.075, n = number of years and Annual payment = $1,500

We substitute these values;

Future Value = $1,500 * {[1+0.075]^20 - 1}/0.075}* (1 + 0.075)

Future value = 1,500 * [1.075]^20 - 1]/0.075 * 1.075

Future Value = $69,829

Thirdly, the total amount of money he would have on both investments at the end of the years later.

Total amount of money = $609,834 + $69,829 = $679,663

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