Math Problem Statement

Angela's bank gave her a 2-year add-on interest loan for $5,360 to pay for new equipment for her antiques restoration business. The annual interest rate is 9.63%. How much interest will she pay? What are her monthly payments?

Solution

The problem you've uploaded involves a 2-year add-on interest loan for $5,360 with an annual interest rate of 9.63%. We need to calculate the total interest she will pay and her monthly payments.

1. Total Interest Paid:

The formula for total interest in an add-on loan is: Total Interest=P×r×t\text{Total Interest} = P \times r \times t Where:

  • P=5,360P = 5,360 (Principal amount),
  • r=9.63%=0.0963r = 9.63\% = 0.0963 (Annual interest rate),
  • t=2t = 2 years (Loan term).

Total Interest=5,360×0.0963×2=1,032.048\text{Total Interest} = 5,360 \times 0.0963 \times 2 = 1,032.048

Rounding to the nearest cent: Total Interest=1,032.05\text{Total Interest} = 1,032.05

2. Total Amount to Repay:

The total amount to be repaid is the sum of the principal and the total interest: Total Repayment=5,360+1,032.05=6,392.05\text{Total Repayment} = 5,360 + 1,032.05 = 6,392.05

3. Monthly Payments:

Since the loan is for 2 years, the number of monthly payments is: Number of Payments=2×12=24\text{Number of Payments} = 2 \times 12 = 24 The monthly payment is: Monthly Payment=Total RepaymentNumber of Payments=6,392.0524=266.3354\text{Monthly Payment} = \frac{\text{Total Repayment}}{\text{Number of Payments}} = \frac{6,392.05}{24} = 266.3354

Rounding to the nearest cent: Monthly Payment=266.34\text{Monthly Payment} = 266.34

Final Answers:

  • She will pay $1,032.05 in interest.
  • Her monthly payments will be $266.34.

Would you like further details or explanations?

Related Questions:

  1. How would the interest change if the interest rate were 12% instead of 9.63%?
  2. What if the loan term was 3 years? How would the monthly payments change?
  3. How would the interest change if the loan amount was $7,000 instead of $5,360?
  4. What is the effective annual rate (EAR) for this loan?
  5. How would the monthly payment change if the loan was repaid quarterly instead of monthly?

Tip: When calculating interest over multiple years, always ensure you're using the correct time period for accurate results.

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Math Problem Analysis

Mathematical Concepts

Simple Interest
Loans
Monthly Payments

Formulas

Total Interest = P × r × t
Monthly Payment = Total Repayment ÷ Number of Payments

Theorems

Simple Interest Theorem

Suitable Grade Level

Grades 9-12