This morning, Clayton deposited $2,500 into an account that pays 5 percent interest, compounded annually. Also this morning, Jayda deposited $2,500 at 5 percent interest, compounded annually. Clayton will withdraw his interest earnings and spend it as soon as possible. Jayda will reinvest her interest earnings into her account. Given this information, which one of the following statements is true?

Question

BlackTom AI · Accepted Answer

Consider the setup: two individuals start with the same deposit of $2,500 at 5% interest, compounded annually. The key difference is how they handle the interest earned.

Option 1: 'After five years, Clayton and Jayda will both have earned the same amount of interest.' This is incorrect because Clayton withdraws his interest each year, so he never compounds his interest and his total interest after five years remains 125 per year, totaling 625. Jayda, by reinvesting, compounds her interest, so her cumulative interest grows faster and will exceed 625 after five years.

Option 2: 'Clayton will earn more interest in Year 3 than Jayda will earn.' In Year 3, Clayton’s interest is 0.05 × 2500 = 125, while Jayda’s Year 3 interest is 0.05 × 2756.25 ≈ 137.81. Therefore, Jayda earns more in Year 3, making this statement false.

Option 3: 'Jayda will earn more interest in Year 1 than Clayton will earn.' In Year 1, both start with 2,500 and both earn 5% of 2,500, which is 125. They earn the same amount in Year 1, so this statement is false.

Option 4: 'Jayda will earn more interest in Year 2 than Clayton will earn.' This is true. Clayton’s Year 2 interest is still 125 (his balance remains 2,500). Jayda’s Year 2 interest is 0.05 × 2625 = 131.25, which is higher than 125. The reinvestment leads to a larger interest amount in Year 2 for Jayda.

Option 5: 'Clayton will earn compound interest.' This is not accurate for Clayton, because he withdraws his interest each year and does not let it compound with his principal. In effect, his calculation is simple interest on the initial principal, not compound interest.

In summary, evaluating each choice shows that the only statement consistent with the described actions is that Jayda will earn more interest in Year 2 than Clayton will earn, due to the compounding effect from reinvesting the interest.

BUSFIN 3220 AU2025 (2110) Exam 1 - Requires Respondus LockDown Browser

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