We are aiming to have $5,000,000 in 45 years and we plan to get there by making monthly investments that are 1% larger than the previous month's investment. Our funds will earn 14.4% compounded monthly. How much should be invested at the end of the first month?

Question

Quizplus · Accepted Answer

The problem can be solved using the future value of a growing annuity formula, which is $FV = P \times \frac{(1 + r)^n - (1 + g)^n}{r - g}$, where $FV$ is the future value, $P$ is the payment at the end of the first period, $r$ is the monthly interest rate, $n$ is the total number of payments, and $g$ is the growth rate of the payment. Given a 14.4% annual interest rate compounded monthly, $r = \frac{14.4\%}{12} = 0.012$, and a growth rate of 1% per month, $g = 0.01$. The total number of payments over 45 years, with 12 payments per year, is $n = 45 \times 12 = 540$. We aim for a future value ($FV$) of $5,000,000. Plugging these values into the formula and solving for $P$ gives us the initial investment amount required to meet the goal.

We Are Aiming to Have $5,000,000 in 45 Years and We