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

Betty will need to deposit $29249.96