Chapter 12.4, Problem 9E

To determine

How much money to be invested in each quarter.

Answer to Problem 9E

The amount of an annuity is $572.34.

Explanation of Solution

The amount of annuity is a sum of all individual payment which is paid for given period with interest. Annuity is sum of money which paid in regular equal payment.

Formula:

Amount of annuity formula is

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

Where,

A = amount of annuity

i = interest rate

n = period

R = regular equal payment

Calculation:

Amount of annuity = $5,000

Interest rate (i) = 10%, $\text{quarter}\text{interest}\text{rate}=\frac{10\%}{4}=2.5\%$

Quarter payment Period (n) = $2\times 4=8$

Calculate the quarter invested amount:

$\begin{array}{c}\text{A=}R\frac{{\left(\text{1+i}\right)}^{\text{n}}-1}{i}\\ \$5,000=R\frac{{\left(\text{1+2}\text{.5\%}\right)}^{\text{8}}-1}{2.5\%}\\ \$5,000=R\times \frac{0.218403}{0.025}\\ \$5,000=R\times 8.736116\\ R=\frac{\$5,000}{8.736116}\\ =\$572.34\end{array}$

Therefore, the invested amount n the quarter is $572.34.