Final answer:
To determine Jordan's monthly car loan payment, we calculate using the formula M = P[r(1+r)^n]/[(1+r)^n – 1]. With a 10% down payment on a $30,000 car and an annual interest rate of 7% compounded monthly for five years, we find the monthly payment after calculating the principal, monthly interest rate, and number of payments.
Step-by-step explanation:
Jordan purchased a car for $30,000 and paid 10% as a down payment. The remaining balance is financed at a 7% annual interest rate compounded monthly for five years. To calculate the monthly payment to settle the loan, we use the formula for the monthly payment (M) on an amortized loan: M = P[r(1+r)^n]/[(1+r)^n – 1], where P is the principal balance, r is the monthly interest rate, and n is the total number of payments.
The down payment is 10% of $30,000, which is $3,000. Thus, the financed amount P is $30,000 - $3,000 = $27,000. The monthly interest rate r is 7% annually, so the monthly interest rate is 7%/12 months = 0.5833%. Converting this to a decimal, we have 0.007 (0.5833 / 100). The total number of payments n for five years is 5 years * 12 months/year = 60 payments.
Using the formula, we calculate the monthly payment as follows: M = $27,000[0.007(1+0.007)^60]/[(1+0.007)^60 – 1]. Solving this yields the monthly payment amount. With this calculation, Jordan can understand the monthly financial commitment required to settle his car loan.