An automobile collector buys an antique car today for $70,000. The collector expects the car to appreciate at the rate of 4% annually for the next 8 years, at which time the collector plans to sell the car for approximately $95,800. Which error was made if the collector can only sell the car for $80,000 in 8 years?

Rationale

Compounding rate was too high.

The collector expected the car to appreciate at a rate of 4% annually, which would project its value to be approximately $95,800 after 8 years. However, selling the car for only $80,000 indicates that the compounded growth was overestimated, leading to the conclusion that the expected appreciation rate was too high.

A (Compounding rate was too high) CORRECT

The collector's expectation of a 4% annual increase led to a projected value of $95,800 after 8 years, which was not realized when the car only sold for $80,000. This discrepancy suggests that the actual appreciation rate was lower than anticipated, confirming that the compounding rate was indeed too high.

B (Discount rate was too high) YOUR ANSWER

A discount rate is used to determine the present value of future cash flows, but in this scenario, the collector is evaluating future value rather than present value. The discussion of a discount rate does not apply directly to the expected appreciation of the car's value, making this choice irrelevant to the error made.

C (Compounding rate was too low) YOUR ANSWER

Selecting a compounding rate that is too low would mean the projected future value would be less than expected. However, the collector's assumption of a 4% rate was too high, not too low, since it resulted in an overestimation of the car’s worth after 8 years.

D (Discount rate was too low) YOUR ANSWER

Similar to option B, the concept of a discount rate does not pertain to the appreciation of the car's value in this scenario. A low discount rate would typically affect present value calculations, which are not relevant to the collector's situation regarding future appreciation.

Conclusion

The collector's error stemmed from overestimating the compounding rate of appreciation for the antique car. While the expected growth was based on a 4% annual appreciation, the actual market value realized after 8 years was significantly lower, indicating that the anticipated rate was too high. Understanding the correct compounding rate is crucial for accurate investment forecasts, particularly in collectibles like antique cars.

Compounding rate was too high.

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