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

Solving for P_0 the last equation, we get:

`P_0=(4700)/((1+(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.