The Phillips family has a joint gross monthly income of $11,300. The $499 lease payment for their car expires in four months. A
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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.
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<u>Before Interest rates Fell</u>
Bond Price = 31 * [( 1 - (1+0.03)^-4) / 0.03] + 1000 / (1+0.03)^4
Bond Price = $1003.717098 rounded off to $1003.72
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<u>After Interest Rates Fell</u>
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
