Question

Twenty-five year old, Howard Wolowitz, would like to become a millionaire. He has decided that he would like to reach this goal when he is fifty-five years old. He invests $7,000 into an account when he is twenty-five years old. The account pays interest at a rate of 7% per year. How much would he have to increase the investment amount each year in order for him to reach his goal? Assume that Howard will not withdraw any money out of the account.

Answer 1

Howard have 25 years to become the millionaire. He invests $7000 in account paying interest of 7% per year. For if the amount is x, which Howard have to increase in the investment amount each year to become millionaire, we have the following equation. It is supposed that Howard doesn't add any amount except the $7000 in the first year, then he adds $x in the second year making principle to be $7000+$x, then again adding $x in the third year making principle to be $7000+$2x and in the 25th year he will have principle of $7000+$24x.

Hence, we have

or

or

or (calculating sum of first 24 natural number by formula )

or .

Hence, approxly $2531.94 is to be added per year to become millionaire in 25 years.