Multiple Choice
If the interest rate on a fixed-payment loan increases while the monthly payment remains the same, what would be the impact on the number of months required to pay off the loan?
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10. Time Value of Money
Time Value of Money Equations
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Ava charges $1,200 to her credit card, which has an annual interest rate of 18% compounded monthly. If she pays off the entire balance in 11 months, how much total interest will she pay?
A
$198.00
B
$108.00
C
$198.72 \times \frac{11}{12} = $182.16
D
$198.72
Verified step by step guidance1
Step 1: Understand the problem. Ava has charged $1,200 to her credit card, which has an annual interest rate of 18% compounded monthly. The goal is to calculate the total interest she will pay if she pays off the balance in 11 months.
Step 2: Convert the annual interest rate to a monthly interest rate. Since the annual interest rate is 18%, divide it by 12 to find the monthly interest rate: \( \text{Monthly Interest Rate} = \frac{18}{12} \% \).
Step 3: Calculate the monthly interest amount. Multiply the principal amount ($1,200) by the monthly interest rate (expressed as a decimal): \( \text{Monthly Interest Amount} = 1200 \times \frac{18}{12} \times \frac{1}{100} \).
Step 4: Determine the total interest for 11 months. Multiply the monthly interest amount by 11: \( \text{Total Interest for 11 Months} = \text{Monthly Interest Amount} \times 11 \).
Step 5: Verify the calculation and compare it to the provided options. Ensure the total interest aligns with the correct answer provided in the problem.
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