Your accountant is suggesting a new financial product that would require an initial investment on your part today of $19,000 and then provide you with a payout of $360,000 in 48 years' time at your retirement. What annually compounded rate of return would you earn in this product?

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BlackTom AI · Accepted Answer

Question restatement: An investment requires an upfront payment of $19,000 today and pays $360,000 at retirement in 48 years. You are asked to find the annually compounded rate of return.

First, set up the compound interest equation for the future value: 19000 × (1 + r)^48 = 360000, where r is the annual rate of return.

Next, isolate the growth factor: (1 + r)^48 = 360000 / 19000 = 18.9473684211.

Take the 48th root to solve for (1 + r): 1 + r = (18.9473684211)^(1/48).

Compute the 48th root by using natural logarithms for accuracy: ln(18.9473684211) ≈ 2.944, divide by 48 to get ≈ 0.06134, and exponentiate: e^(0.06134) ≈ 1.0633.

Thus, r ≈ 1.0633 − 1 = 0.0633, or about 6.33% per year, when rounded to two decimal places. With more precise calculation, you obtain approximately 6.3202%.

Note on answer options: The provided data block lacks explicit answer choices to evaluate individually. In a typical multiple-choice scenario, you would compare the computed rate to each option and select the one that matches. Here, the mathematically obtained rate is around 6.3202%, which would be the correct choice if presented.

Summary of key steps:
- Formulate the future value equation: 19000(1 + r)^48 = 360000.
- Solve for (1 + r) by taking the 48th root of 360000/19000.
- Subtract 1 to get the annual rate r; result is approximately 6.3202%.

FINC5001 (ND) Quiz 1

Your accountant is suggesting a new financial product that would require an initial investment on your part today of $19,000 and then provide you with a payout of $360,000 in 48 years' time at your retirement. What annually compounded rate of return would you earn in this product?

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FINC5001 (ND) Quiz 1

Your accountant is suggesting a new financial product that would require an initial investment on your part today of $19,000 and then provide you with a payout of $360,000 in 48 years' time at your retirement. What annually compounded rate of return would you earn in this product?

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