Question

Shelby obtains an installment loan to purchase a small plane for $20,000. Her down payment is 20% and the APR is 12% for 30 months.
Find the
a. down payment
b. amount of the loan
c. monthly payment
d. finance charge

Answer 1

Part of the amount is paid at the start which reduces the finance charge

(interest paid) for the loan.

Correct responses (approximate) values:

(a) $4,000

(b) $16,000

(c) $619.97

(d) $2,599.09

Methods used to calculate the payments for the loan

The price of the small plane = $20,000

The down payment for the plane = 20% of the price

Annual Percentage Rate, APR, of the loan, r = 12% = 0.12

Duration of payment for the loan = 30 months

a. The down payment = 20% of $20,000, which gives

• $Down \ payment = \mathbf{\dfrac{20}{100} \times \ 20,000} = \underline{ \ 4,000}$

b. Amount of the loan = Plane price - Down payment

Therefore;

• Amount of the loan, P = $20,000 - $4,000 = $16,000

c. The monthly payment, is given as follows;

$M = \mathbf{ \dfrac{P \cdot \left(\dfrac{r}{12} \right) \cdot \left(1 + \dfrac{r}{12} \right)^n}{\left(1 + \dfrac{r}{12} \right)^n - 1 }}$

Which gives;

$M = \mathbf{\dfrac{16,000 \times \left(\dfrac{0.12}{12} \right) \times \left(1 + \dfrac{0.12}{12} \right)^{30} }{\left(1 + \dfrac{0.12}{12} \right)^{30} - 1 }} \approx 619.97$

• The monthly payment, M = $619.97

d. Finance charge = Total payment - Loan amount

Therefore;

Finance charge ≈ 30 × 619.97 - 16,000 = 2,599.09

• The finance charge is approximately $2,599.09

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