Question

A $ 1 comma 000 bond with a coupon rate of 6.2​% paid semiannually has two years to maturity and a yield to maturity of 6​%. If interest rates fall and the yield to maturity decreases by​ 0.8%, what will happen to the price of the​ bond?

Answer 1

Answer:

As a result of a fall in interest and YTM, the bond price will increase by $15.04

Explanation:

To calculate the change in price due to fall in interest rate, we must first calculate the price of the bond before and after the fall of interest rates.

To calculate the price of the bond, we need to first calculate the coupon payment per period. We assume that the interest rate provided is stated in annual terms. As the bond is a semi annual bond, the coupon payment, number of periods and semi annual YTM will be,

Coupon Payment (C) = 1000 * 0.062 * 0.5 = $31

Total periods (n)= 2 * 2 = 4

r or YTM = 6% * 1/2 = 3% or 0.03

The formula to calculate the price of the bonds today is attached.

Before Interest rates Fell

Bond Price = 31 * [( 1 - (1+0.03)^-4) / 0.03]  +  1000 / (1+0.03)^4

Bond Price = $1003.717098 rounded off to $1003.72

After Interest Rates Fell

New YTM = 6% - 0.8%   =  5.2% or 0.052

Semi Annual YTM = 0.052 * 0.5  = 0.026

Bond Price = 31 * [( 1 - (1+0.026)^-4) / 0.026]  +  1000 / (1+0.026)^4

Bond Price = $1018.764647 rounded off to $1018.76

Change in Bond Price = 1018.76 - 1003.72   = $15.04

As a result of a fall in interest and YTM, the bond price increased by $15.04