A loan of $1000 at 5% annual compound interest; what is the total amount after 2 years?

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Multiple Choice

A loan of $1000 at 5% annual compound interest; what is the total amount after 2 years?

Explanation:
With annual compounding, you grow the amount by a factor of 1 plus the interest rate each year. Use P(1 + r)^t. Here P = 1000, r = 0.05, t = 2, so the amount is 1000 × (1.05)^2 = 1000 × 1.1025 = 1102.50. You can also see this by applying the growth year by year: 1000 becomes 1050 after the first year, then 1050 becomes 1102.50 after the second year. The other numbers come from incorrect approaches (like simple interest or not compounding), but the correct total with annual compounding is 1102.50.

With annual compounding, you grow the amount by a factor of 1 plus the interest rate each year. Use P(1 + r)^t. Here P = 1000, r = 0.05, t = 2, so the amount is 1000 × (1.05)^2 = 1000 × 1.1025 = 1102.50. You can also see this by applying the growth year by year: 1000 becomes 1050 after the first year, then 1050 becomes 1102.50 after the second year. The other numbers come from incorrect approaches (like simple interest or not compounding), but the correct total with annual compounding is 1102.50.

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