If Zach takes out a \$10,000 loan at an annual interest rate of 6% for 5 years with monthly payments, what percentage of his total first-year payments is paid as interest?

• A. Approximately 35%
• B. Approximately 25%
• C. Approximately 10%
• D. Approximately 55%

Answer: (D)

Verified step by step guidance

1. Step 1: Calculate the monthly interest rate by dividing the annual interest rate by 12. Use the formula: \( \text{Monthly Interest Rate} = \frac{\text{Annual Interest Rate}}{12} \).
2. Step 2: Determine the monthly payment amount using the loan amortization formula: \( M = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1} \), where \( M \) is the monthly payment, \( P \) is the loan principal, \( r \) is the monthly interest rate, and \( n \) is the total number of payments (months).
3. Step 3: Calculate the total payments made in the first year by multiplying the monthly payment amount by 12 (since there are 12 months in a year).
4. Step 4: Compute the total interest paid in the first year. For each monthly payment, the interest portion is calculated as \( \text{Interest} = \text{Remaining Loan Balance} \cdot \text{Monthly Interest Rate} \). Sum up the interest amounts for all 12 months.
5. Step 5: Determine the percentage of the total first-year payments that is paid as interest. Use the formula: \( \text{Percentage of Interest} = \frac{\text{Total Interest Paid in First Year}}{\text{Total Payments Made in First Year}} \cdot 100 \).