Chapter 12.4, Problem 15E

To determine

The amount of each payment.

Answer to Problem 15E

The present value of annuity is $307.24.

Explanation of Solution

The present value of annuity is the current value of a pre planned cash flow in the future, given specified discount rate or rate of return.

Formula:

Present value of annuity formula:

$\text{Present}\text{value}\text{of}\text{annuity}=R\frac{1-{\left(\text{1}+i\right)}^{-\text{n}}}{i}$

Where,

i = interest rate

n = period

R = regular equal payment

Calculation:

Given information:

Borrowing amount = $12,000

Interest rate (i) = $10\frac{1}{2}\%$

Period (n) = 4

Calculate the amount of each payment:

$\begin{array}{c}\text{Borrowing}\text{amount =}R\frac{1-{\left(\text{1+i}\right)}^{-\text{n}}}{i}\\ \$12,000=\text{R}\times \frac{1-{\left(\text{1+}\frac{\text{10}\frac{1}{2}\%}{12}\right)}^{-\text{12}\times \text{4}}}{\frac{\text{10}\frac{1}{2}\%}{12}}\\ \$12,000=\text{R}\times \frac{1-{\left(\text{1+}\frac{10.50\%}{12}\right)}^{-\text{12}\times \text{4}}}{\frac{10.50\%}{12}}\end{array}$

Simplify further as follows.

$\begin{array}{c}\$12,000=\text{R}\times \frac{1-{\left(\text{1+}\frac{10.50\%}{12}\right)}^{-48}}{\frac{10.50\%}{12}}\\ \$12,000=\text{R}\times \frac{1-{1.00875}^{-48}}{0.00875}\\ \$12,000=\text{R}\times \frac{0.341752}{0.00875}\\ R=\frac{\$12,000}{39.05734}\\ R=\$307.24\end{array}$

Therefore, amount of each payment is $307.24.