What is the future value of $3,088 invested for 10 years at 6.1 percent compounded annually?

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BlackTom AI · Accepted Answer

Question restatement: What is the future value of $3,088 invested for 10 years at 6.1 percent compounded annually?

Option A: $4,151.97. This value is too high if you only consider simple growth for 10 years at a bit over 6%, and it doesn’t align with the power of compounding. Using the correct compound formula would give a higher result than simple interest, not this amount.

Option B: $5,582.53. This is the correct ballpark for compounding 3,088 at 6.1% for 10 years. The calculation uses FV = PV × (1 + r)^n, so FV = 3,088 × (1.061)^10. Since (1.061)^10 is approximately 1.808, the product is about 3,088 × 1.808 ≈ 5,582.

Option C: $4,170.20. This value could come from misapplying the interest rate or treating the growth as if it were simple interest, or using an incorrect exponent, leading to a smaller final amount than actual compound growth.

Option D: $9,763.51. This is far too large for 10 years at 6.1% on a principal of only 3,088; it would require a much higher rate or an error in formula application (such as inadvertently squaring the growth or compounding more than 10 years).

Option E: $10,092.18. Similar to D, this overestimates the result significantly for the given rate and time, suggesting a miscalculation or misinterpretation of the compounding period.

Synthesis: The correct approach is to apply the compound interest formula FV = PV × (1 + r)^n with PV = 3,088, r = 0.061, n = 10. Numerically, (1.061)^10 ≈ 1.808, and multiplying by 3,088 yields approximately 5,582.53. The other options deviate from this value due to misapplication of the formula (simple interest, incorrect exponent, or impractically large growth).

What is the future value of $3,088 invested for 10 years at 6.1 percent compounded annually?

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