To calculate the total amount Juan must pay back, including interest, we need to use the formula for compound interest:
1. First, calculate the monthly interest rate by dividing the annual interest rate by 12 (since it's compounded monthly):
Annual interest rate = 8.5%
Monthly interest rate = 8.5% / 12 = 0.7083%
2. Next, calculate the total number of compounding periods over 3 years (36 months):
Number of compounding periods = 3 years * 12 months/year = 36 months
3. Now, use the compound interest formula to find the total amount Juan must pay back:
Total amount = Principal * (1 + Monthly interest rate)^Number of compounding periods
4. Substitute the values into the formula:
Principal = $2,000
Monthly interest rate = 0.7083%
Number of compounding periods = 36 months
5. Calculate the total amount Juan must pay back, including interest:
Total amount = $2,000 * (1 + 0.7083%)^36
6. Compute the total amount using the formula:
Total amount = $2,000 * (1 + 0.007083)^36
7. After performing the calculations, the total amount Juan must pay back, including interest, is the final answer.
