To determine how much Mason owes on his car loan after 16 months, we first need to calculate his monthly payment using the loan details, and then find out how much he has paid so far and the remaining balance after 16 months.
Step 1: Calculate the Monthly Payment
Mason's car loan:
- Principal (P): $41,217
- Annual Interest Rate (r): 5.40% or 0.054
- Loan Term (t): 6 years = 72 months
The monthly interest rate (i) can be calculated as:
The formula for the monthly payment (M) on an amortizing loan is:
is the total number of payments (72 months).
Substituting the values:
Calculating
Now substituting this back into the formula:
So, the monthly payment
Step 2: Total Paid After 16 Months
Now, we need to calculate how much Mason has paid after 16 months:
Step 3: Remaining Balance After 16 Months
Next, we calculate the remaining balance after 16 months of payments. This can be calculated using the loan amortization formula:
The remaining balance (B) of a loan after
is the number of payments made (16).
Substituting the values:
Answer
Thus, after 16 months, Mason owes approximately $32,229.01 on his loan.