Stephanie purchased an antique necklace six years ago for $300 as an investment.The clasp was repaired at the end of the second year for $150.The repaired necklace has just sold at auction for $850.What is the average compound annual rate of return that was earned by investing in this collectible?

Question

Quizplus · Accepted Answer

First, we need to calculate the total cost of the investment which includes the cost of the necklace and the repair cost:
Total Cost = Purchase Price + Repair Cost
Total Cost = $300 + $150
Total Cost = $450

Next, we need to calculate the total return on the investment which includes the sale price and any repair costs:
Total Return = Sale Price - Repair Cost
Total Return = $850 - $150
Total Return = $700

Now we can calculate the average annual rate of return using the following formula: 
[(Ending value / Beginning value) ^ (1 / number of years)] - 1
[(Total Return + Total Cost) / Total Cost) ^ (1 / 6)] - 1
[($1150 / $450) ^ (1 / 6)] - 1
[2.5558] - 1
1.5558

Finally, we need to convert this rate to a compound annual rate of return:
Compounded Annual Rate of Return = (1 + Annual Rate of Return) ^ n - 1
Compounded Annual Rate of Return = (1 + 1.5558) ^ 1/6 - 1
Compounded Annual Rate of Return = 12.54%

Therefore, the answer is C) 12.54.

Stephanie Purchased an Antique Necklace Six Years Ago for $300