Question

Suppose that you invest in a two-year Treasury bond with a coupon rate of 7% and $1,000 par. Suppose that you buy this bond at a price of exactly $1,000. You intend to hold this bond to maturity and reinvest the coupons until the bond matures. You expect to reinvest the coupons in an account that pays an APR of 1.26%, with semi-annual compounding. What is the effective annual rate of return on your investment? Hint: see Example 8 in the Lecture. Do not round at intermediate steps in your calculation. Express your answer in percent. Round to three decimal places. Do not type the % symbol. If the return is negative, then include a minus sign.

Answer 1

APR is the annual percentage rate that incorporates not just the interest but any additional cost of borrowing as well which in this case will be the cost borne by the bank in procuring the funds/deposit.

Par Value of Bond = $1000

Coupon Rate = 7% or 0.07

APR = 1.26% (This is the interest to be received annually)

The effective annual rate of return can be calculated using the following formula:

= (1 + Nominal Rate/ No. of compounding period)^{(no. of compounding period)} - 1

= ( 1 + 0.0126/2)⁽²⁾ - 1

= [ (1.0063)² - 1

= 0.01263969

Also, the coupon rate so earned will be a return on your investment so we shall calculate the effective annual rate on the bond investment as well, which is same as 7%. The same is shown below:

= (1 + 0.07)¹ - 1 = 0.07 or 7%

Total, effective annual rate of return on investment = (0.07 + 0.01263969) = 0.008263969 or 8.264%