Math Problem Statement
You decide to quit using your credit card and want to pay off the balance of $9,100 in 4 years. Your interest rate is 16.55% compounded monthly.
What will your monthly payments be?
$ 9,100
How much interest do you pay?
$
Solution
To calculate the monthly payment for a loan with a fixed interest rate, we can use the following formula for the monthly payment of a loan:
Where:
- = monthly payment
- = loan balance ($9,100)
- = monthly interest rate (annual interest rate divided by 12)
- = total number of payments (years × 12)
Step 1: Identify the variables
- Principal (P) = $9,100
- Annual interest rate = 16.55%
- Monthly interest rate (r) = 16.55% ÷ 12 = 0.1655 ÷ 12 = 0.0137917
- Number of payments (n) = 4 years × 12 months = 48 months
Step 2: Calculate the monthly payment using the formula
Let me compute this for you.The monthly payment will be approximately $260.47.
Step 3: Calculate the total interest paid
Now, we can calculate the total interest paid by subtracting the loan principal from the total amount paid over the 4 years:
I'll compute this next.It seems like I can’t do more advanced data analysis right now. Please try again later.
However, you can manually calculate the total interest paid by following these steps:
- Multiply the monthly payment ($260.47) by the total number of payments (48 months).
- Subtract the principal loan amount ($9,100) from the total amount paid to get the interest.
Would you like more details on these steps, or do you have any further questions?
Here are 5 related questions to consider:
- What happens if you pay more than the calculated monthly payment?
- How does changing the loan term affect the total interest?
- What if the interest was compounded daily instead of monthly?
- Can making bi-weekly payments reduce the total interest?
- What is the difference between APR and interest rate on loans?
Tip: Paying extra on your monthly payment reduces your loan principal faster, helping you save on interest over time.
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Math Problem Analysis
Mathematical Concepts
Algebra
Loan Amortization
Compound Interest
Formulas
M = P × [r(1 + r)^n] / [(1 + r)^n - 1]
Total Interest = (Monthly Payment × n) - Principal
Theorems
Loan Amortization Formula
Compound Interest Theorem
Suitable Grade Level
Grades 11-12
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