Question

What is the price of a zero-coupon ($1,000 par value) bond that matures in 17 years has a promised yield of 9.5%? The bond's price is $ . (Round to the nearest cent.)

Answer 1

Price of a bond is the present value of all future cash flows receivable from the bond discounted at required rate of return

Future cash flows are periodic interest payments and maturity value of the bond

A zero coupon bond has no interest payments and has only maturity value which is equal to the face value. So, price of a zero coupon bond will be calculated by calculating the discounting factor or present value factor and multiplying the same with the face value

Present value factor

= 1 / ( 1 + Rate of interest ) ^ Number of years

= 1 / ( 1 + 9.5 / 100 ) ^ 17

= 1 / (1.095 ^ 17)

= 1 / 4.677783

= 0.213776

So, Price of the bond

= Face Value x PV Factor

= $1,000 x 0.213776

= $ 213.7