Your Dad just gave you $20,000 to invest for your retirement. You want to manage your money well and invest it safely. You believe that you can earn 7% per annum in a safe investment. How much money will you have in 45 years time?

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Question restatement: You are given $20,000 to invest for retirement and expect a safe return of 7% per year for 45 years. What will the investment be worth at the end of 45 years?

Options: 
- a. $420,049
- b. $63,000
- c. $420,000
- d. $98,049
- e. $61,600

Approach and calculation:
- The future value of a lump-sum investment is FV = PV × (1 + r)^t, where PV = 20,000, r = 0.07, t = 45.
- Compute (1.07)^45. A common way is to use natural logs: ln(1.07) ≈ 0.06766, so 45 × ln(1.07) ≈ 3.0447. exponentiating gives e^(3.0447) ≈ 20.99. Thus (1.07)^45 ≈ 20.99.
- Multiply by the present value: 20,000 × 20.99 ≈ 419,800.

Option-by-option assessment:
- Option a: $420,049. This value is extremely close to the calculated ≈ $419,800. The small difference (~$249) is due to rounding during the (1.07)^45 approximation or using a slightly different calculator/precision.
- Option b: $63,000. This is far too small for 45 years at 7% growth on $20,000; even without compounding, doubling would require more than that, so this is not plausible.
- Option c: $420,000. This is also a plausible near target and matches the general magnitude. It is very close to the computed value (~$419,800), differing by about $200.
- Option d: $98,049. This is inconsistent with compound growth at 7% for such a long horizon; it would imply a much smaller growth factor than (1.07)^45.
- Option e: $61,600. This is even farther off and would correspond to an almost negligible growth, which contradicts the substantial 45-year horizon at 7% annually.

Why the correct choice (in numerical terms) is the best match: The calculated future value sits near $420,000. Among the options, both a and c lie in that vicinity, with a offering a value that aligns more precisely with the standard FV calculation after accounting for typical rounding. The other options are orders of magnitude off and do not reflect the expected growth over 45 years at 7% annual interest.

Summary: The problem requires applying the compound interest formula FV = PV × (1 + r)^t and then comparing the resulting numeric value to the given options. The option that best matches the computed future value—while recognizing minor rounding differences—is the one around $420,000.

ACCT 3380 R10 SPRING 2025 Module 5 (2nd half): Practice Questions, Due Sunday 11PM

Your Dad just gave you $20,000 to invest for your retirement. You want to manage your money well and invest it safely. You believe that you can earn 7% per annum in a safe investment. How much money will you have in 45 years time?

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ACCT 3380 R10 SPRING 2025 Module 5 (2nd half): Practice Questions, Due Sunday 11PM

Your Dad just gave you $20,000 to invest for your retirement. You want to manage your money well and invest it safely. You believe that you can earn 7% per annum in a safe investment. How much money will you have in 45 years time?

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

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