Question

Vicky bought a car priced at $9748 for 7% down and equal quarterly payments for 4 years. If interest is 12% compounded monthly what is the size of the quarterly payment?

Answer 1

To find the size of the quarterly payment for Vicky's car loan, calculate the loan amount after the down payment and use the formula for equal quarterly payments. The size of the quarterly payment is $842.12.

Step-by-step explanation:

To find the size of the quarterly payment, we need to calculate the loan amount after the down payment and then use the formula for calculating the equal quarterly payments.

1. Calculate the down payment: $9748 * 0.07 = $682.36
2. Calculate the loan amount: $9748 - $682.36 = $9065.64
3. Convert the annual interest rate to a monthly interest rate: 12% / 12 = 1%
4. Convert the interest rate to decimal form: 1% = 0.01
5. Calculate the number of quarterly payments: 4 years * 4 quarters = 16 quarters
6. Calculate the size of the quarterly payment using the formula: Size of Quarterly Payment = Loan Amount * Monthly Interest Rate / (1 - (1 + Monthly Interest Rate)^(-Number of Quarterly Payments))

Plugging in the values, we get: Size of Quarterly Payment = $9065.64 * 0.01 / (1 - (1 + 0.01)^(-16)) = $842.12