Question

A mutual fund pays 15% compounded monthly. How much should I invest now so that 22 months from now I will have $4700 in the account?

Answer 1

To solve this problem, we will use the formula for compound interest:

$P_N=P_0\cdot(1+\frac{r}{k})^{N\cdot k}.$

Where:

• P_N is the amount of money after N years,

,

• P_0 is the initial amount of money,

,

• r is the interest in decimals,

,

• k is the number of compounded periods.

In this case, we have:

• P_N = $4700,

,

• r = 15% = 0.15,

,

• k = 12 (because the interest is compounded monthly),

,

• N = 22/12 (we divide the # of months by the # of months in a year).

Replacing these data in the formula above, we have:

$\begin{gathered} 4700=P_0\cdot(1+\frac{0.15}{12})^{\frac{22}{12}\cdot12}, \\ 4700=P_0\cdot(1+\frac{0.15}{12})^{22}.^{} \end{gathered}$

Solving for P_0 the last equation, we get:

$P_0=\frac{4700}{(1+\frac{0.15}{12})^{22}}\cong3576.08.$

We found that the initial amount of money must be $3576.08.

Answer

I must invest $3576.08 now so that 22 months from now I will have $4700 in the account.