Chapter 12.4, Problem 3E

To determine

To find: The amount of annuity for the given data.

Answer to Problem 3E

The amount of annuity is $13,180.79.

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:

It is given that annual payment (R) is $1,000, interest rate (i) is 6% and period (n) is 10 years.

Calculation of the amount of an annuity:

$\begin{array}{c}\text{A=}\text{R}\times \frac{{\left(\text{1+i}\right)}^{\text{n}}-1}{i}\\ =\$1,000\times \frac{{\left(\text{1}+\text{6\%}\right)}^{\text{10}}-1}{6\%}\\ =\$13,180.79\end{array}$

Therefore, amount of interest is $13,180.79.