Question 3

The compounding rate was too high.

The collector anticipated that the antique car would appreciate to approximately $95,800 after 8 years based on a 4% annual appreciation. However, if the actual sale price is only $80,000, this indicates that the expected compounding rate was overestimated.

A) Compounding rate was too high

This option correctly identifies the error made by the collector. The expectation of a 4% annual appreciation led the collector to project a future value of $95,800, which was not achieved. The reality of selling the car for $80,000 suggests that the growth rate was indeed too optimistic.

B) Discount rate was too high

This option is incorrect in this context. A discount rate pertains to the present value calculations, not the appreciation of an asset over time. Since the question focuses on the appreciation of the car's value, this option does not apply.

C) Compounding rate was too low

This choice is incorrect as well. If the compounded growth had been too low, the actual value of the car would have been less than anticipated, leading to an even lower sale price than $80,000. The collector expected a higher value based on a 4% rate, indicating that the compounding rate was not low enough.

D) Discount rate was too low

This option does not apply to the scenario presented. A low discount rate would not affect the appreciation rate of the car; rather, it would influence the present value of future cash flows. The focus here is on the appreciation rate rather than how the value is discounted.

Conclusion

The correct answer, A, highlights that the collector's expectation of a 4% compounding rate was too high, resulting in a projected value that was unrealistic. All other options fail to address the error in the appreciation forecast, as they relate to discount rates or misinterpret the nature of the compounding effect on value.