Conrad has $10,000; he is considering whether to (1) invest in a mutual fund with an 8% annual interest rate or (2) remodel his kitchen. If he remodels the kitchen, he will be able to sell his home for an additional $13,000 when he moves at the end of five years. Which of the following statements is (are) TRUE?
I. The net present value of remodeling the kitchen is -$1,152.42.
II. Conrad is better off investing his money in the mutual fund.
III. If Conrad invests in the mutual fund, his money will grow to $10,800 at the end of five years, making this a worse investment than the kitchen remodel.

Question

Quizplus · Accepted Answer

I is true because the net present value (NPV) of remodeling the kitchen, considering the future value of $13,000 after five years and discounting it back at the 8% annual interest rate, is indeed negative, indicating that the investment in the kitchen remodel results in a loss compared to keeping the money invested at 8%. II is true because, with an 8% annual interest rate, investing $10,000 will yield more than the net gain from the kitchen remodel over the same period, making the mutual fund a better financial decision. III is false because the calculation provided is incorrect; at an 8% annual interest rate compounded annually, $10,000 will grow to more than $10,800 in five years. The correct future value using the formula FV = PV(1 + r)^n, where PV = $10,000, r = 0.08, and n = 5, is approximately $14,693.28, making the mutual fund investment better than the kitchen remodel.

Conrad Has $10,000; He Is Considering Whether to (1) Invest