You have $10,000 and wish to invest it for the future. How much money will you have if you invest it for 5 years with a bank at 6% interest rate, compounded monthly (rounded to the nearest dollar)?

Question

BlackTom AI · Accepted Answer

We start by identifying the key elements of the problem: principal P = 10,000, annual nominal rate r = 6% compounded monthly, so the monthly rate is 0.06/12 = 0.005. The number of compounding periods over 5 years is n = 5 × 12 = 60. The future value formula for monthly compounding is FV = P × (1 + i)^n, where i is the monthly rate.

Option A: $13,382. Here, the value is noticeably lower than the expected outcome. If we plug in the numbers, FV ≈ 10,000 × (1.005)^60. Since (1.005)^60 is greater than 1.34, a value as low as 1.338 would imply (1.005)^60 ≈ 1.333, which isn’t consistent with the accumulation from six percent per year compounded monthly for five years. Therefore this is too small.

Option B: $13,488. This matches the computed future value when using the exact formula FV = 10,000 × (1.005)^60 and rounding to the nearest dollar. The monthly compounding at 0.5% for 60 periods grows the principal to just under 13.5k, and 13,488 is a plausible and commonly cited rounded result for these inputs.

Option C: $13,500. While close to the expected amount, rounding to this exact figure would require the precise FV to be at least 13,500 when rounded. If the true FV is around 13,488, rounding to the nearest dollar would not reach 13,500. This is slightly high for the given inputs.

Option D: $12,382. This is significantly lower than the starting principal, which would imply a loss or negative growth scenario. With positive interest compounded monthly, the future value must exceed 10,000, so this option is clearly incorrect.

To summarize the reasoning, we apply FV = 10,000 × (1.005)^60, evaluate that expression numerically, and then compare each option against the result. The correct rounded value in this standard calculation aligns with $13,488, while the other choices either underestimate, overestimate beyond reasonable rounding, or contradict the basic principle that compound interest at a positive rate grows the principal.

You have $10,000 and wish to invest it for the future. How much money will you have if you invest it for 5 years with a bank at 6% interest rate, compounded monthly (rounded to the nearest dollar)?单项选择题

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