Question

Betty wants to retire in 45 years. She needs $2,000,000. If she’s able to find a Mutual Fund that offers 9.5% interest and compounds quarterly, how much will she need for a deposit?

Answer 1

Let's begin by listing out the information given to us:

Time (t) = 45 years

Amount (A) = $2,000,000

Interest (r) = 9.5% = 0.095

Compounds (n) = Quarterly = 4

This is compound interest and is given by the formula:

$\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ 2000000=P(1+\frac{0.095}{4})^{4\cdot45} \\ 2000000=P(1+0.02375)^{180} \\ P=\frac{2000000}{(1+0.02375)^{180}}=29249.96 \\ P=\text{ \ }29249.96 \end{gathered}$

Betty will need to deposit $29249.96