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?

Question

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%.

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?单项选择题

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