Question

5. Consider a bond paying a coupon rate of 9% per year semiannually when the market interest rate is only 6%. The bond has five years until maturity. (15 points) a. Find the bond’s price today and six months from now after the next coupon is paid. b. What is the total rate of return on the bond?

Answer 1

Calculation of purchase price of bond

face value = 1000

market Interest rate (i) = 6%

semi Annual rate 6%/2= 3%

Coupon rate = 9%

Semiannual coupon rate( 4.50%

Coupon Amount = 1000*4.5%= 45

Years to maturity (n)= 5 years

Semiannual periods (n) =5*2= 10

Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n

45*(1-(1/(1+3%)^10))/3% + 1000/(1+3%)^10

1127.953043

So, bond price or purchase price shall be $ 1127.95

Calculation of price of sale

face value = 1000

market Interest rate (i) = 6%

semi Annual rate 6%/2= 3%

Coupon rate = 9%

Semiannual coupon rate( 4.50%

Coupon Amount = 1000*4.5%= 45

Years to maturity (n)= 4.5 years

Semiannual periods (n) =5*2= 9

Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n

45*(1-(1/(1+3%)^9))/3% + 1000/(1+3%)^9

1116.791634

So, bond price or sale price shall be $ 1116.79

Rate of return formula = (Sale price - purchase price+coupon received)/Purchase price*12/no. of months

One coupon received = $45

so, annual rate of return = (1116.79-1127.95+45)/1127.95 *12/6

0.06 or 6%

So, Total rate of return on bond is 6% annual