Please determine the total cost of repaying a $750 credit card loan with a 17.99% interest rate compounded monthly and a fixed monthly payment over a period of 9 months
To determine the total cost of repaying a $750 credit card loan over a period of 9 months with a 17.99% interest rate compounded monthly, we need to calculate the monthly payment amount and then multiply it by the number of months.
Step 1: Calculate the monthly interest rate.
The monthly interest rate is calculated by dividing the annual interest rate by 12.
Monthly interest rate = 17.99% / 12 = 1.4992%
Step 2: Calculate the monthly payment amount using the loan repayment formula.
Let P be the principal amount (loan amount) of $750.
Let r be the monthly interest rate in decimal form (1.4992% / 100).
Let n be the number of periods (9 months).
The formula to calculate the fixed monthly payment amount is:
Monthly payment = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
Monthly payment = 750 * (0.014992 * (1 + 0.014992)^9) / ((1 + 0.014992)^9 - 1) ≈ $86.91
Step 3: Calculate the total cost by multiplying the monthly payment by the number of months.
Total cost = Monthly payment * Number of months
Total cost = $86.91 * 9 months = $782.19
Therefore, the total cost of repaying a $750 credit card loan with a 17.99% interest rate compounded monthly and a fixed monthly payment over a period of 9 months is approximately $782.19.
Im sorry to disturb you but that was wrong
Apologies for the mistake. Let's recalculate:
The correct formula for calculating the fixed monthly payment amount is:
Monthly payment = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
Using the given values:
P = $750 (principal amount)
r = 17.99% / 12 = 0.1799 / 12 = 0.014992 (monthly interest rate)
n = 9 (number of months)
Monthly payment = 750 * (0.014992 * (1 + 0.014992)^9) / ((1 + 0.014992)^9 - 1)
Monthly payment ≈ $88.11
Now we can calculate the total cost:
Total cost = Monthly payment * Number of months = $88.11 * 9 months = $792.99
Therefore, the correct total cost of repaying a $750 credit card loan with a 17.99% interest rate compounded monthly and a fixed monthly payment over a period of 9 months is approximately $792.99.