Chapter 3, Problem 66RE

Solution

To find: the future value FV accumulated in an annuity.

  $FV=R\frac{{\left(1+\frac{r}{k}\right)}^{kt}-1}{\frac{r}{k}}$

Given information:

The given information is: “periodic payments R for t years are invested at an annual interest rate r , with payments made and interest credited k times per year”

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:

By the above definition, 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: $FV=R\frac{{\left(1+i\right)}^n-1}{i}$

Here, the interest rate i per compounding period (payment interval) is:

  $i=\frac{r}{k}$

And the number of payments is:

  $n=k\cdot t$

So, the future value FV accumulated in an annuity is:

  $FV=R\frac{{\left(1+\frac{r}{k}\right)}^{kt}-1}{\frac{r}{k}}$