A 30-year zero coupon bond with a face value of $5,000 is currently selling for $1,156.88 and has a market rate of interest of 5%. Using the bond's modified duration, what is the approximate change in the price of the bond if interest rates fall to 4.25%

Price will increase by $277.58

Explanation:

Market rate of Interest of a zero coupon bond can be determined by following formula

Market Rate of Interest = [ (F / P) ^ (1/30) ] - 1

4.25% = [ ($5000 / P) ^ (1/30) ] - 1

0.0425 + 1 = ($5000 / P) ^1/30

(1.0425) ^30 = (($5000 / P) ^1/30) ^30

3.4856 = $5000 / P

P = $5,000 / 3.4856

P = $1,434.46

Now Calculate the change in Price

Change in price = $1,434.46 - $1,156.88 = $277.58

Price will increase by $277.58