Meredith is starting a cleaning business with a 3 year loan of 10,000 at a 5 percent compound annual interest rate. Assuming the loan is not paid back in full until the end of year 3, how much will she owe at the end?

Meredith is starting a cleaning business with a 3 year loan of 10,000 at a 5 percent compound annual interest rate. Assuming the loan is not paid back in full until the end of year 3, how much will she owe at the end?

• A. 11,000
• B. 11,576.25
• C. 15,000
• D. 12,500

Answer: (B)

Compound interest grows the amount owed when you don’t make payments. With annual compounding, the amount after n years is the principal times (1 + rate)^n. Here the principal is 10,000, the rate is 5% (0.05), and the loan isn’t repaid for 3 years, so the amount owed is 10,000 × (1.05)^3. Calculating (1.05)^3 gives 1.157625, and multiplying by 10,000 yields 11,576.25. You can also see this by iterating year by year: 10,000 → 10,500 after year one, → 11,025 after year two, → 11,576.25 after year three. This matches 11,576.25. The other numbers would come from simple interest or different time frames, not from three years of compounding at 5%.

Compound interest grows the amount owed when you don’t make payments. With annual compounding, the amount after n years is the principal times (1 + rate)^n. Here the principal is 10,000, the rate is 5% (0.05), and the loan isn’t repaid for 3 years, so the amount owed is 10,000 × (1.05)^3. Calculating (1.05)^3 gives 1.157625, and multiplying by 10,000 yields 11,576.25. You can also see this by iterating year by year: 10,000 → 10,500 after year one, → 11,025 after year two, → 11,576.25 after year three. This matches 11,576.25. The other numbers would come from simple interest or different time frames, not from three years of compounding at 5%.