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?

Question

BlackTom AI · Accepted Answer

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.

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?单项选择题

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