Question at position 3 If $1,000 is invested for 2 years at 6% compounded quarterly, then the compound amount at the end of the period is$1593.84.$1126.49.$1120.00.$1141.23.$1123.60.

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Question at position 3 If $1,000 is invested for 2 years at 6% compounded quarterly, then the compound amount at the end of the period is$1593.84.$1126.49.$1120.00.$1141.23.$1123.60.

BlackTom AI · Accepted Answer

First, identify the key values: principal P = 1000, annual nominal rate r = 6%, compounded quarterly, so the quarterly rate is r/4 = 0.06/4 = 0.015 (1.5%). The compounding frequency is quarterly for 2 years, giving n = 2 × 4 = 8 periods.

Option A: $1593.84. This would imply a much larger growth than 1.5% per quarter for 8 periods. If we try to reach this amount, the effective growth factor would be 1593.84/1000 ≈ 1.59384 over 8 periods, which corresponds to an average per-period growth far above 1.015. This is inconsistent with the given rate, so this option is incorrect.

Option B: $1126.49. This is close to the calculated amount when using the exact formula A = P(1 + r/4)^{8} = 1000(1.015)^8. Computing (1.015)^8 yields approximately 1.12649, and multiplying by 1000 gives about 1126.49. This matches the standard compound-interest calculation for the given data, so this option is plausible and likely correct.

Option C: $1120.00. This would correspond to a growth factor of 1.12 over 8 periods, i.e., an average per-period increase around 1.5% but slightly less precise than the exact calculation. Since the exact calculation yields about 1.12649, 1120.00 is too small by about 6.49, indicating a mismatch with the correct compounding formula.

Option D: $1141.23. This amount would require a larger growth than the exact (1.015)^8 factor provides. It would correspond to an effective total factor of 1.14123 over 8 periods, which is not consistent with a steady 1.5% per quarter, so this option is incorrect.

Option E: $1123.60. This is again a bit lower than the exact 1126.49, suggesting a growth factor of 1.1236. Since the precise calculation with 1.015 for eight periods yields about 1.12649, this value is not aligned with the standard formula and is therefore incorrect.

In summary, evaluating each choice against the compound-interest formula A = P(1 + 0.06/4)^{8} shows that only the amount near 1126.49 aligns with the correct calculation for 1000 invested at 6% compounded quarterly over 2 years. The remaining options either overstate or understate the growth and do not fit the given rate and compounding structure.

Question at position 3 If $1,000 is invested for 2 years at 6% compounded quarterly, then the compound amount at the end of the period is$1593.84.$1126.49.$1120.00.$1141.23.$1123.60.

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