Math Problem Statement

Match each of the Pairs of Years and Percentage (ex. 15, 4%) with their correct Monthly Payment and Total Interest. 20 years, 7%

Solution

To calculate the monthly payment and total interest for a loan of 20 years at an interest rate of 7%, we need to use the amortization formula for monthly payments.

The formula for monthly payments MM on a loan is:

M=P×r(1+r)n(1+r)n1M = P \times \frac{r(1 + r)^n}{(1 + r)^n - 1}

Where:

  • PP is the loan principal (the total amount borrowed).
  • rr is the monthly interest rate (annual rate divided by 12).
  • nn is the total number of monthly payments (loan term in years multiplied by 12).

To calculate total interest, we need: Total Payments=M×n\text{Total Payments} = M \times n Total Interest=Total PaymentsP\text{Total Interest} = \text{Total Payments} - P

Could you provide the loan amount or principal for the calculation? If not, I can help explain the general approach and calculate an example.

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Math Problem Analysis

Mathematical Concepts

Loan Amortization
Interest Calculation
Monthly Payments

Formulas

Monthly Payment Formula: M = P * [r(1 + r)^n] / [(1 + r)^n - 1]
Total Payments Formula: Total Payments = M * n
Total Interest Formula: Total Interest = Total Payments - P

Theorems

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Suitable Grade Level

Grades 10-12