Steve purchased a bond for $975.00.Ninety days later he received interest income of $40.00,and then immediately sold the bond for $990.00.What is the annualized rate of return Steve earned on this investment?
A) 5.6%
B) 22.6%
C) 16.4%
D) 10.1%
E) 12.3%

Question

Quizplus · Accepted Answer

Steve's total return from the bond is the sum of the interest income and the capital gain. The interest income is $40, and the capital gain is the difference between the sale price ($990) and the purchase price ($975), which is $15. Therefore, the total return is $40 + $15 = $55. The initial investment was $975, so the return as a percentage of the investment is ($55 / $975) * 100 = 5.64%. However, this return was achieved over 90 days, not a year. To annualize the return, we use the formula for annualizing returns over periods shorter than a year: Annualized Return = (Return over period + 1)^(365/Days in period) - 1. Plugging in the numbers: Annualized Return = ((55/975) + 1)^(365/90) - 1 ≈ 22.6%.

Steve Purchased a Bond for $975