Final answer:
To determine the future cost of a $90,000 house with a 4% annual appreciation rate over 6 years, we use the formula for compound interest. After calculating, the future value is found to be $113,878.71, which does not match the provided multiple-choice options.
Step-by-step explanation:
To find out what a $90,000 house will cost 6 years from now with an appreciation rate of 4% compounded annually, we use the formula for compound interest: FV = P(1 + r/n)^(n*t), where FV is the future value, P is the principal amount ($90,000), r is the annual interest rate (0.04), n is the number of times that interest is compounded per year (1 for annually), and t is the time in years (6).
Substituting the values, we get FV = $90,000(1 + 0.04/1)^(1*6), which simplifies to FV = $90,000(1 + 0.04)^6. Therefore, FV = $90,000(1.04)^6.
Calculating this gives us FV = $90,000 * 1.265319 = $113,878.71.
However, this result does not match any of the answer choices provided by the student. It's possible there may have been a miscalculation or typo in the options given. The correct approach to finding the future cost of the house with compound appreciation has been demonstrated above.