Math Problem Statement
Taylor took out a student loan for $6,000 and agreed to pay it off with monthly payments over 11 years at a 5% interest rate compounded monthly. This made her monthly payments $59. How much will Taylor end up paying in interest?
Solution
To calculate how much Taylor will pay in interest, we can use the following steps:
- Find the total amount paid over the loan term by multiplying the monthly payment by the number of months.
- Subtract the original loan amount from the total amount paid to determine the interest paid.
Step 1: Calculate the total number of payments
Taylor is making monthly payments over 11 years, so:
Step 2: Calculate the total amount paid
Taylor's monthly payment is $59, and she makes 132 payments:
Step 3: Calculate the interest paid
The total interest paid is the difference between the total amount paid and the original loan amount:
So, Taylor will end up paying $1,788 in interest over the course of the loan.
Would you like more details or have any questions?
Here are 5 related questions:
- What would happen if the interest rate were higher?
- How would shortening the loan term affect monthly payments?
- How can Taylor reduce the total interest paid on the loan?
- What if she made extra payments—how much could she save in interest?
- How would switching to a bi-weekly payment schedule impact the total interest?
Tip: Paying a little extra each month can significantly reduce the overall interest paid on a loan.
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Math Problem Analysis
Mathematical Concepts
Loan Amortization
Interest Calculation
Compound Interest
Formulas
Total Payments = Monthly Payment × Number of Months
Interest Paid = Total Payments - Principal Amount
Theorems
Loan amortization formula
Suitable Grade Level
Grades 10-12
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