You purchased a five-year annual payment 6 percent coupon bond for $1,000 and you planned on holding it to maturity. However,right after you bought the bond,it was called at $1,043.29 when all interest rates fell to 5 percent and remained there for the full five years. You reinvested the money for the full five years. What was your annual compound rate of return off your original investment?

Question

Quizplus · Accepted Answer

The initial investment was $1,000 and the bond was called at $1,043.29, so the capital gain is $43.29. The annual interest payment is 6% of $1,000, which is $60. Since the bond was held for only one year, the reinvestment return for the remaining four years needs to be taken into consideration.

Using the future value formula, we can find the value of the reinvestment at the end of the five years as follows:

$1,000 x (1 + 0.05)^4 = $1,215.51

The total future value of the investment at the end of five years is:

$43.29 + ($60 x 5) + $1,215.51 = $1,583.79

The annual compound rate of return is the rate that would turn the initial investment of $1,000 into $1,583.79 over five years.

Using the compound interest formula, we can solve for the rate:

$1,583.79 = $1,000 x (1 + r)^5

(1 + r)^5 = 1.58379

1 + r = (1.58379)^(1/5)

1 + r = 1.0589

r = 0.0589 or 5.89%

Therefore, the annual compound rate of return off the original investment is 5.89%, which is choice (B).

You Purchased a Five-Year Annual Payment 6 Percent Coupon Bond