If $2,000 is invested at 5% annual compound interest for 3 years, what is the amount?

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Multiple Choice

If $2,000 is invested at 5% annual compound interest for 3 years, what is the amount?

Explanation:
With annual compound interest, each year’s interest is added to the balance, so the amount after t years is P(1 + r)^t. Here P is 2000, r is 0.05, and t is 3. Calculate step by step: after the first year, 2000 × 1.05 = 2100. After the second year, 2100 × 1.05 = 2205. After the third year, 2205 × 1.05 = 2315.25. So the amount after 3 years is 2315.25. This matches the correct choice because it uses the compound growth factor (1.05)^3 rather than simply adding 5% each year. If you used simple interest, you'd have 2000 × (1 + 0.05 × 3) = 2300, which is not the same as compounding. The other numbers don’t reflect the exact compounded growth.

With annual compound interest, each year’s interest is added to the balance, so the amount after t years is P(1 + r)^t. Here P is 2000, r is 0.05, and t is 3.

Calculate step by step: after the first year, 2000 × 1.05 = 2100. After the second year, 2100 × 1.05 = 2205. After the third year, 2205 × 1.05 = 2315.25.

So the amount after 3 years is 2315.25. This matches the correct choice because it uses the compound growth factor (1.05)^3 rather than simply adding 5% each year. If you used simple interest, you'd have 2000 × (1 + 0.05 × 3) = 2300, which is not the same as compounding. The other numbers don’t reflect the exact compounded growth.

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