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.

PMGT2850 (ND) Class Quiz 1

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)?

查看解析

登录即可查看完整答案

类似问题

Part 1Consider a twominus−year investment: Given a constant and positive interest rate, the interest earned in the second year will be greater than the interest earned in the first year (assuming annual compounding). Part 1 True False

If Jack and Jill deposit $1,000 into a savings account that earns 4.5% annual interest (compounded monthly), how long will it take for their money to double to $2,000?

How much will you get back on a five year investment of $100 that pays 5% interest per year?

What is the effective yield (APY) if the Annual Percentage Rate (APR) is 7.64 percent and it is compounded quarterly?

If you deposit $10,000 in an account with an annual rate of 9% compounded semiannually, how long will it take for you to have $2,000,000 in the account?

In order to determine the future value of some lump sum, we must use the process of ________.

With compound interest, the investor earns interest on the principal amount invested plus interest on accumulated interest. Which of the following compounding frequencies would yield the investor the greatest ending balance assuming all else is equal?

You have located an investment that pays 9 percent per year. You invest $800. How much will you have in seven years? Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.Blank.xlsx

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

PMGT2850 (ND) Class Quiz 1

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)?

查看解析

登录即可查看完整答案

类似问题

Part 1Consider a twominus−year ​investment: Given a constant and positive interest​ rate, the interest earned in the second year will be greater than the interest earned in the first year​ (assuming annual​ compounding). Part 1 True False

If Jack and Jill deposit $1,000 into a savings account that earns 4.5% annual interest (compounded monthly), how long will it take for their money to double to $2,000?

How much will you get back on a five year investment of $100 that pays 5% interest per year?

What is the effective yield (APY) if the Annual Percentage Rate (APR) is 7.64 percent and it is compounded quarterly?

If you deposit $10,000 in an account with an annual rate of 9% compounded semiannually, how long will it take for you to have $2,000,000 in the account?

In order to determine the future value of some lump sum, we must use the process of ________.

With compound interest, the investor earns interest on the principal amount invested plus interest on accumulated interest. Which of the following compounding frequencies would yield the investor the greatest ending balance assuming all else is equal?

You have located an investment that pays 9 percent per year. You invest $800. How much will you have in seven years? Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.Blank.xlsx

更多留学生实用工具

希望你的学习变得更简单

Part 1Consider a twominus−year investment: Given a constant and positive interest rate, the interest earned in the second year will be greater than the interest earned in the first year (assuming annual compounding). Part 1 True False