Question

Nathan Reynolds bought a car for $15,000. He made a down payment of $3,000. Nathan secured a loan for the balance of the purchase price at 8 percent interest for four years.

determine the monthly payment and total interest

Answer 1

1) The monthly payment is approximately $292.96

2) The total interest is approximately $2,061.84

Explanation:

1) The financing method Nathan Reynolds applied to buy the car is given as follows;

The purchase price of the car = $15,000

The down payment made for the car = $3,000

The

The interest on the loan he took for the balance of the purchase price, R = 8%

The number of years for which he took the loan, n = 4 years = 48 months

We have;

The balance of the purchase price = (The purchase price of the car) - (The down payment made for the car)

∴ The balance of the purchase price = $15,000 - $3,000 = $12,000

The balance of the purchase price = $12,000 = The loan Nathan secured

The monthly payment on a loan is given by the following formula

`A = P * (r \cdot (1 + r)^n)/((1 + r)^n - 1)`

Where;

A = The payment amount made monthly

P = The principal or loan amount = $12,000

r = The interest rate divided by 12 = R/12 = 8/12 = 2/3

n = The number of months the monthly payment will be made = 48 months

By plugging in the variable values, we get;

`A = 12,000 * ((2)/(300) * \left (1 + (2)/(300) \right ) ^(48))/( \left (1 + (2)/(300) \right )^(48) - 1) = 292.955068099 \approx 292.96`

Therefore, the payment amount made monthly, A ≈ $292.96

2) The total payment made in the 48 months = A × 48 = 292.955068099 × 48 ≈ 14,061.84

The total payment made in the 48 months ≈ $14,061.84

The total interest = (The total payment made in the 48 months) - (The loan amount)

∴ The total interest = $14,061.84 - $12,000 ≈ $2,061.84