Question

A $ 1000 bond with a coupon rate of 6​% paid semiannually has eight years to maturity and a yield to maturity of 9​%. If interest rates rise and the yield to maturity increases to 9.3​%, what will happen to the price of the​ bond?

Answer 1

Formula to calculate price of bond
Price of bond	Coupon amount*(1-(1+r^-n)/r)) + Face value*(1/(1+r^n)
where r is interest rate and n is number of years
Calculation of current price of bond when Yield to maturity is 9%
Semi-annual coupon amount	$30.00	1000*(6%/2)
Semi-annual YTM	4.50%	9%/2
No of payments	16	8*2
Price of bond	30*(1-(1.045^-16))/0.045 + 1000*(1/(1.045^16)
Price of bond	30*11.23402+1000*0.494469
Price of bond	$831.49
Calculation of current price of bond when Yield to maturity is 9.30%
Semi-annual coupon amount	$30.00	1000*(6%/2)
Semi-annual YTM	4.65%	9.30%/2
No of payments	16	8*2
Price of bond	30*(1-(1.0465^-16))/0.0465 + 1000*(1/(1.0465^16)
Price of bond	30*11.11289+1000*0.48325
Price of bond	$816.64
Increase in interest rate would lead to decrease in price of bond by $14.85 (831.49-816.4)