Chapter 12.4, Problem 21E

To determine

The actual price of JN’s car.

Answer to Problem 21E

The purchase price is $9,020.60.

Explanation of Solution

Loan amount is an amount which can be borrowed for specific period of time and is expected to be paid back with interest.

Formula to calculate loan amount:

$\text{Monthly}\text{payment}\text{=}\frac{i\times \left(\text{Loan amount}\right)}{1-{\left(1+i\right)}^{-n}}$

Where,

i = interest amount

$A_p$ = loan amount

$n$= period

Given:

Monthly payment:  $220

Period: 3 year

Total number of payment: $3\times 12=36\text{ Ttimes}$

Interest rate: 8%

Calculation:

Calculate the loan amount of the car.

$\begin{array}{c}\text{Monthly}\text{payment}\text{=}\frac{i\times \left(A_p\right)}{1-{\left(1+i\right)}^{-n}}\\ \$220=\frac{\frac{8\%}{12}\times \left(A_p\right)}{1-{\left(1+\frac{8\%}{12}\right)}^{-3\times 12}}\\ \$220=\frac{0.006666667\times \left(A_p\right)}{1-{\left(1+\frac{8\%}{12}\right)}^{-3\times 12}}\\ \$220=\frac{0.006666667\times \left(A_p\right)}{0.21275537}\end{array}$

$\begin{array}{c}0.006666667\times \left(A_p\right)=46.8039\\ \left(A_p\right)=\frac{46.8039}{0.006666667}\\ =\$7,020.60\end{array}$

Therefore, the loan amount is $7,020.60.

Calculate purchase price of car.

$\begin{array}{c}\text{Purchase}\text{price}=\text{Loan}\text{amount}+\text{Down}\text{payment}\\ =\text{\$7,020}\text{.606}+\text{\$2,000}\\ =\text{\$9,020}\text{.60}\end{array}$

Therefore, the purchase price of JN’s car is $9,020.60.