Final answer:
To calculate Chantal's monthly moped payment, we subtract the down payment from the purchase price to find the financed amount, then apply the loan formula using the monthly interest rate and the total number of payments, resulting in a monthly payment of approximately $29.68.
Step-by-step explanation:
The subject of this question is Mathematics, specifically focusing on the finance topic of calculating loan payments. The question involves Chantal purchasing a moped with a down payment and financing the remaining balance with an interest rate that is compounded monthly.
To calculate the monthly payment Chantal will have to make, we use the formula for the monthly payment P on a loan, which is P = (r*PV) / (1 - (1 + r)^(-n)), where PV is the present value of the loan (amount financed), r is the monthly interest rate, and n is the total number of payments (number of months).
First, we calculate the amount financed (PV), which is the total cost of the moped minus the down payment:
- Total moped cost = $1875.47
- Down payment = $650
- Amount financed (PV) = $1875.47 - $650 = $1225.47
Next, we convert the annual interest rate to a monthly interest rate:
- Annual interest rate = 6.6%
- Monthly interest rate (r) = 6.6% / 12 = 0.55%
- Monthly interest rate in decimal = 0.55% / 100 = 0.0055
Finally, we determine the number of payments:
- Number of years = 4
- Number of months (n) = 4 * 12 = 48
Plugging the values into the payment formula gives us:
P = (0.0055*1225.47) / (1 - (1 + 0.0055)^(-48))
Using a calculator, we find that Chantal's monthly payment is approximately $29.68.