Math Problem Statement

a. What is her monthly payment? b. What is the total of all her monthly payments? c. What is the total finance charge?

Solution

Based on the information in the image, let's analyze each part:

  1. Monthly Payment Calculation (Part a): To calculate her monthly payment for an installment loan, we typically need:
    • The principal loan amount.
    • The annual percentage rate (APR) or interest rate.
    • The loan term in months.

Since I can't see specific numerical values in the image, let’s assume general variables and solve with the following formula:

Monthly Payment=P×r1(1+r)n\text{Monthly Payment} = \frac{P \times r}{1 - (1 + r)^{-n}}

where:

  • PP is the loan principal,
  • rr is the monthly interest rate (annual rate divided by 12),
  • nn is the number of payments (loan term in months).

Once I know the specific values, I can provide the exact monthly payment.

  1. Total of All Monthly Payments (Part b): Once the monthly payment (MM) is known, the total amount of all monthly payments over the term is:

Total Payments=M×n\text{Total Payments} = M \times n

  1. Total Finance Charge (Part c): The finance charge is the total interest paid over the loan term. It is calculated as the difference between the total of all monthly payments and the original loan principal:

Finance Charge=Total PaymentsP\text{Finance Charge} = \text{Total Payments} - P

If you provide specific values, I can calculate these answers exactly.

Do you need clarification on any part or specific calculations?

Here are five related questions:

  1. How does an increase in the interest rate affect monthly payments?
  2. How would a longer loan term impact the finance charge?
  3. What’s the difference between a fixed-rate and variable-rate loan?
  4. How can paying extra on each installment reduce the total finance charge?
  5. What are some strategies to reduce monthly payments without extending the loan term?

Tip: To reduce total finance charges, consider paying off the loan early if there’s no prepayment penalty.

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Math Problem Analysis

Mathematical Concepts

Loan Amortization
Interest Calculation
Finance Charges

Formulas

Monthly Payment = (P * r) / (1 - (1 + r)^(-n))
Total Payments = Monthly Payment * n
Finance Charge = Total Payments - Principal

Theorems

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Suitable Grade Level

Grades 10-12