Question

A rich uncle wants to make you a millionaire how much money must he deposit in a trust fund paying 12% compounded quarterly at the time of your birth to yield $1 million when you retire at age 58 round your answer to the nearest cent

Answer 1

If one fixes the initial balance $P_0$ , the nominal interest rate $r$ and the duration of the deposit $T$ (in years), you earn more interest with more compounding periods per year $K$. The number of compounding periods that make up $T$ will be $KT$. Then we use the formula

$P_{KT}=P_0(1+\frac{r}{K})^{KT}$

In our case, $r=0.12, K=4, KT=58\cdot 4=232, P_{KT}=1,000,000$.

Therefore, we have that $1,000,000=P_0(1+\frac{0.12}{4})^{232}=P_0(1.03)^{232}=951.12179\cdot P_0$, and consequently, $P_0=\frac{1,000,000}{951.12179}=1,051.39$.

Answer: a rich uncle must deposit in a trust fund $1,015.39 to make you a millionaire when you retire at age 58.