Question

What is the percentage change in price for a zero coupon bond if the yield changes from 6.5 % to 5.5%? The bond has a face value of $1,000 and it matures in 10 years. Use the price determined from the first yield, 6.5 %, as the base in the percentage calculation. The percentage change in the bond price if the yield changes from 6.5% to 5.5% is nothing __________%. (Round to two decimal places.)

Answer 1

Price of a Zero-Coupon Bond is the Present Value of the Face Value of the Bond

Price of the Zero-Coupon Bond at 6.50% Yield to Maturity

Price of the Bond = Face Value / (PVIF 6.50%, 10 Years)

= Face Value x [1 / (1 + r) ⁿ]

= $1,000 x [1/(1 + 0.065)¹⁰]

= $1,000 / 1.87714

= $532.73

Price of the Zero-Coupon Bond at 5.50% Yield to Maturity

Price of the Bond = Face Value / (PVIF 5.50%, 10 Years)

= Face Value x [1 / (1 + r) ⁿ]

= $1,000 x [1/(1 + 0.055)¹⁰]

= $1,000 / 1.70814

= $585.43

The percentage change in the bond price

Percentage change in the bond price = [($585.43 - $532.73) / $532.73] x 100

= [$52.70 / $532.73] x 100

= 9.89%

“Therefore, The percentage change in the bond price = 9.89%”