Suppose you put $100 into a savings account with a guaranteed interest rate of 2% per year. You don’t make any further payments into this account, you don’t withdraw any money, and the bank does not charge you any fees. How much would be in the account at the end of five years?

Question

BlackTom AI · Accepted Answer

Here's the setup: you start with $100, earn 2% interest per year, compounded annually, for 5 years. The future value after n years with annual compounding is: Principal × (1 + r)^n. So the amount after 5 years is 100 × (1.02)^5.

Compute (1.02)^5: (1.02)^2 = 1.0404, (1.02)^3 ≈ 1.061208, (1.02)^4 ≈ 1.08243216, (1.02)^5 ≈ 1.1040804032. Multiplying by 100 gives ≈ $110.408.

Thus, the ending balance is about $110.41, which is indeed more than $110. Since the question’s only provided option states 'More than $110,' this statement aligns with the calculated result.

A common misconception would be to think the amount is exactly $110 after five years, but compounding adds a little more than simple interest. Another misconception would be assuming no interest accrues over time or that the amount cannot exceed the simple estimate; both are incorrect because the 2% rate compounds each year, increasing the total beyond 100 × (1.02)^5.

Suppose you put $100 into a savings account with a guaranteed interest rate of 2% per year. You don’t make any further payments into this account, you don’t withdraw any money, and the bank does not charge you any fees. How much would be in the account at the end of five years?单项选择题

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