The outstanding balance on Peter's credit card account is 4730 dollars. The bank issuing the credit card is charging 19.3 percent of interest per year compounded monthly. If Peter decides to pay off his balance in equal monthly installments at the end of each month for the next 15 months, how much will be his monthly payment?
To calculate Peter's monthly payment, we need to use the formula for a loan payment with compound interest.
The formula is:
P = (r * PV) / (1 - (1 + r)^(-n))
Where:
P = monthly payment
r = monthly interest rate
PV = present value or outstanding balance
n = total number of months
First, let's calculate the monthly interest rate. We divide the annual interest rate by 12 (number of months).
r = 19.3% / 12 = 0.0193 / 12 = 0.0016083 (approximately)
Now we can substitute the values into the formula:
P = (0.0016083 * 4730) / (1 - (1 + 0.0016083)^(-15))
Using a calculator, we can solve this equation to find the monthly payment.