Chapter 13, Problem 1ECP

To determine

The value of annuity after amount of payment $\$4,500$ is made annually for $10$ years at $3\%$ interest rate with the help of table $13.1$.

Answer to Problem 1ECP

The value of annuity after $10$ years on an ordinary annuity of $\$4,500$ made annually at $3\%$ is $\underset{\_}{\$51,587.55}$.

Explanation of Solution

Procedure used:

Calculating future value of an ordinary annuity by table lookup:

$1$ Firstly, determine the number of periods and rate per period.

$2$ Search the calculated periods and rate in the ordinary annuity table to get the value for table factor at intersection for future value of $\$1$.

$3$ Perform multiplication of payment with table factor’s each period.

$\begin{array}{ccc}\begin{array}{l}\text{Future}\text{value}\text{of}\\ \text{an}\text{ordinary}\text{annuity}\end{array}& =& \begin{array}{l}\text{Annuity}\text{payment each period}\times \\ \text{Ordinary}\text{annuity}\text{table}\text{factor}\end{array}\end{array}$

Calculation:

Calculate the number of periods and rate per period as follows.

$\begin{array}{c}\text{Periods}=10\times 1\\ =10\end{array}$

$\begin{array}{c}\text{Rate}=3\%÷1\\ =3\%\end{array}$

The table factor at intersection of $10$ periods and $3\%$ rate in the ordinary annuity table $13.1$ is $11.4639$.

Perform multiplication of table factor $11.4639$ with the payment $\$4,500$ as, $\$4,500\times 11.4639=51,587.55$.

Therefore, the value of annuity after $10$ years on an ordinary annuity of $\$4,500$ made annually at $3\%$ is $\underset{\_}{\$51,587.55}$.