An investment of $2,000 earns 5% interest compounded annually for two years. What is the amount after two years?

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Multiple Choice

An investment of $2,000 earns 5% interest compounded annually for two years. What is the amount after two years?

Explanation:
When interest is compounded annually, each year’s 5% is earned on the balance at the end of that year, not just on the original principal. Start with 2,000. After one year: 2,000 × 1.05 = 2,100. After the second year: 2,100 × 1.05 = 2,205. Using the compound formula, A = P(1 + r)^t = 2,000 × (1.05)^2 = 2,000 × 1.1025 = 2,205. So the amount after two years is 2,205 dollars. The other options come from either skipping interest or misapplying the interest rate (simple vs. compound).

When interest is compounded annually, each year’s 5% is earned on the balance at the end of that year, not just on the original principal. Start with 2,000. After one year: 2,000 × 1.05 = 2,100. After the second year: 2,100 × 1.05 = 2,205. Using the compound formula, A = P(1 + r)^t = 2,000 × (1.05)^2 = 2,000 × 1.1025 = 2,205. So the amount after two years is 2,205 dollars. The other options come from either skipping interest or misapplying the interest rate (simple vs. compound).

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