Question

Both Bond Bill and Bond Ted have 9.6 percent coupons, make semiannual payments, and are priced at par value. Bond Bill has 6 years to maturity, whereas Bond Ted has 23 years to maturity. Both bonds have a par value of 1,000. If interest rates suddenly rise by 3 percent, what is the percentage change in the price of these bonds?

Answer 1

Bond Bill's percentage change = -12.37℅

Bond Ted's percentage change = -22.37℅

Step-by-step explanation:

Both Bonds are priced at $1000 now and an increase of 3℅ interest rate occurs.

A) For Bond Bill:

•New yield will be = 9.6℅ + 3℅ = 12.6℅

• Semi annual yield = 12.6/2 = 4.8℅

• Number of periods = 6years * 2payments per year = 12

• Coupon = 1000 *9.6/2 = 48

With a 3℅ increase rate, the price of bond Bill will be

PV(6.3℅, 12, -48, -1000)

= 987.63

Therefore, ℅ change =

(987.63 - 1000) / 1000

= -12.37℅

Bond Bill's percentage change= -12.37℅

B) To calculate For Bond Ted:

•New yield will be = 9.6℅ + 3℅ = 12.6℅

• Semi annual yield = 12.6/2 = 4.8℅

• Number of periods = 23years * 2payments per year = 46

• Coupon = 1000 * 9.6/2 = 48

With a 3℅ increase rate, the price of bond Ted will be:

PV(6.3℅, 46, -48, -1000)

= 977.63

Therefore, ℅ change will be:

(977.63 - 1000) / 1000

= -22.37℅

Bond Ted's ℅ change = -22.37℅