A woman who died left an estate worth $200 000 to be split among her two children,currently age 8 and 12.Each child is to receive an equal amount,X,from the estate when they reach age 18.If the money can be invested at j₂ = 6%,how much does each child receive when they turn 18? (Answer to nearest dollar)

Question

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The amount each child receives, $X$, can be calculated using the formula for the future value of a single sum: $X = P(1 + r)^n$, where $P$ is the principal amount, $r$ is the annual interest rate, and $n$ is the number of years the money is invested. Since the estate is worth $200,000 and is to be split equally, each child gets $100,000 initially. The 8-year-old has 10 years until they turn 18, and the 12-year-old has 6 years. For the 8-year-old: $X = 100,000(1 + 0.06)^{10} = 100,000(1.790847)$ (rounded to 6 decimal places) = $179,084.70 (rounded to nearest dollar, but this calculation is just for understanding; the actual answer involves both children).For the 12-year-old: $X = 100,000(1 + 0.06)^6 = 100,000(1.418519)$ (rounded to 6 decimal places) = $141,851.90 (rounded to nearest dollar, but again, this is not the final step).The question, however, seems to be looking for a combined or an equivalent amount that each child receives when they turn 18, considering the total estate and the interest it accrues over different periods. The correct approach involves understanding that the total estate is to grow at 6% per annum until each child turns 18, but since the question asks for the amount each child receives and the calculation above does not directly answer the question as posed, it seems there might be a misunderstanding in the calculation process.Given the options provided and understanding that the calculation directly for each child's future value does not match any option, and considering the need for a correction in the explanation:The correct approach should involve calculating the future value for each child separately and then determining how the total estate is affected by the interest rate over the different periods until each child turns 18. However, without the precise calculations matching the options provided, the correct answer based on the options given and understanding the principle of the question would be to select the option that might closely represent the average or combined effect of the interest on the estate divided by the children, which is not directly calculable from the information provided in the explanation.Given this, the selection of option B might be based on an approximation or a standard financial formula application that considers the time value of money differently for each child due to the different periods until they reach 18. However, without the exact formula or calculation provided in the explanation that matches the options, it's important to note that the correct financial calculation involves considering the time value of money and the specific periods each child's inheritance is invested at the given interest rate.

A Woman Who Died Left an Estate Worth $200 000