Question

A bond with a coupon rate of 5.72 percent and semiannual coupon payments matures in 24 years. The YTM is 6.79 percent. What is the effective annual yield?

Answer 1

The effective annual yield (EAY) for the bond is 7.05%.

Step-by-step explanation:

The effective annual yield (EAY) is a measure of the total return an investor can expect to receive from a bond investment in one year.

To calculate the effective annual yield, we need to consider the number of coupon payments per year and the yield to maturity (YTM) of the bond. In this case, the bond has a coupon rate of 5.72% and semiannual coupon payments, so there are 2 coupon payments per year.

The YTM is 6.79%.

The formula for calculating the effective annual yield is:

EAY = (1 + YTM/n)^n - 1

where YTM is the yield to maturity and n is the number of coupon payments per year.

Using the given values, we can calculate:

EAY = (1 + 0.0679/2)^2 - 1 = 0.0705 or 7.05%

Therefore, the effective annual yield for the bond is 7.05%.

Answer 2

5.80%

Step-by-step explanation:

Effective annual yield is used to calculate a coupon bond return assuming the coupons are reinvested.

With 5.72 % coupon bond, compounded semiannually, you use the following formula to calculate the effective annual yield;

effective annual yield
`=(1+(r)/(m)) ^(m) -1`

r = the nominal coupon rate = 5.72%

m = compounding periods in a year = 2

Next, plug in the numbers to the formula;

effective annual yield
`=(1+(0.0572)/(2) )^(2) -1\\ \\ =1.05802 -1\\ \\ =0.05802`

= 5.80%