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?

A) $24.29
B) $68.82
C) $103.74
D) $425.16
E) $801.93

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.