Chapter 3.6, Problem 50E

Solution

To find: what should be J’s monthly payment to achieve her goal.

$239.42

Given information:

J wants to accumulate $250,000 in 20 years by contributing in a fund that earns 12.4% annual interest.

Formula Used:

Future Value of an Annuity

The future value FV of an annuity consisting of n equal periodic payments of R dollars at an interest rate i per compounding period (payment interval) is:

  $FV=R\frac{{\left(1+i\right)}^n-1}{i}$

Explanation:

The data given is:

  $FV=\$250,000,r=12.4\%,t=20,k=12$

Here, the interest is credited 12 times a year, so the interest rate is:

  $\begin{array}{c}i=\frac{r}{k}\\ =\frac{0.124}{12}\end{array}$

The number of payments is:

  $\begin{array}{c}n=k\cdot t\\ =12\cdot 20\\ =240\end{array}$

Let her monthly payment be $ R .

Substitute these values in the above formula,

  $\begin{array}{c}FV=R\frac{{\left(1+i\right)}^n-1}{i}\\ 250000=R\cdot \frac{{\left(1+\frac{0.124}{12}\right)}^{240}-1}{\frac{0.124}{12}}\\ 250000=R\left(1044.22\right)\end{array}$

  $\begin{array}{c}R=\frac{250000}{1044.22}\\ R\approx \$239.42\end{array}$

J’s monthly payment should be $239.42.