Math Problem Statement

Kyle used the Quantitative Reasoning Process to create a plan to pay off his student loans of $8,060. The interest rate on his loan is 3.3% annually and he plans to make monthly payments of $78.95 for 10 years. Complete months 1 and 2 of the amortization table below.

How much of Kyle's payment goes to Interest in Month 2?

Solution

To find out how much of Kyle's payment goes to interest in Month 2, we first need to understand how amortization works. Each monthly payment consists of two parts: interest and principal. The interest for each month is calculated based on the remaining loan balance.

Let's follow these steps to calculate the interest portion of the payment for Month 2:

Step 1: Monthly Interest Rate Calculation

The annual interest rate is 3.3%. To find the monthly interest rate: Monthly interest rate=Annual interest rate12=3.3%12=0.275%=0.00275\text{Monthly interest rate} = \frac{\text{Annual interest rate}}{12} = \frac{3.3\%}{12} = 0.275\% = 0.00275

Step 2: Month 1 Interest and Principal

  • Initial Loan Balance: $8,060
  • Monthly Payment: $78.95

Interest for Month 1: Interest for Month 1=Loan Balance×Monthly Interest Rate=8,060×0.00275=22.165\text{Interest for Month 1} = \text{Loan Balance} \times \text{Monthly Interest Rate} = 8,060 \times 0.00275 = 22.165

Principal for Month 1: Principal for Month 1=Monthly PaymentInterest for Month 1=78.9522.165=56.785\text{Principal for Month 1} = \text{Monthly Payment} - \text{Interest for Month 1} = 78.95 - 22.165 = 56.785

Remaining Balance after Month 1: Remaining Balance=8,06056.785=8,003.215\text{Remaining Balance} = 8,060 - 56.785 = 8,003.215

Step 3: Month 2 Interest and Principal

  • New Loan Balance: $8,003.215

Interest for Month 2: Interest for Month 2=New Loan Balance×Monthly Interest Rate=8,003.215×0.00275=22.0088\text{Interest for Month 2} = \text{New Loan Balance} \times \text{Monthly Interest Rate} = 8,003.215 \times 0.00275 = 22.0088

The interest portion of the payment for Month 2 is $22.01 (rounded to two decimal places).

Conclusion

In Month 2, $22.01 of Kyle's payment goes towards interest.

Would you like more details on any part of this calculation, or do you have any other questions?

Here are five related questions that might interest you:

  1. How much of Kyle's payment goes towards the principal in Month 2?
  2. What is the remaining balance after Month 2?
  3. How does the interest portion of the payment change over time?
  4. What would be the total interest paid over the 10 years?
  5. How would an increase in the monthly payment affect the loan payoff period?

Tip: Always check the remaining balance each month to ensure that the interest and principal portions are correctly applied to your loan payments.

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Math Problem Analysis

Mathematical Concepts

Amortization
Interest Calculation
Loan Payment

Formulas

Monthly Interest Calculation

Theorems

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Suitable Grade Level

Grades 9-12