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.

Question

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.

查看解析

登录即可查看完整答案

类似问题

Bob bought some land costing $14,990. Today that same land is valued at $55,000. How long has Bob owned this land if the price of land has been increasing at 6 percent per year?

If $5200 is placed in an account which pays 7% per annum, compounding annually, then the balance in the account after n years is calculated by:

Question at position 2 How long will it take for $600 to amount to $900 at an annual rate of 6% compounded quarterly?5 years, 3 months8 years, 1 month6 years, 9 1/2 months7 years, 2 months

Your great aunt Matilda put some money in an account for you on the day you were born. This account pays 8% interest per year. On your 21st birthday the account balance was $5033.83. The amount of money that would be in the account if you left the money there until your 65th birthday is closest to:

Your great aunt Matilda put some money in an account for you on the day you were born. This account pays 8% interest per year. On your 21st birthday the account balance was $5033.83. The amount of money that your great aunt Matilda originally put in the account is closest to:

Claire’s coin collection contains fifty 1948 silver dollars. Her grandparents purchased them at their face value in 1948. These coins have appreciated by 7.6 percent annually. How much is the collection expected to be worth in 2025?

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单