Question

Calculate the price of a zero-coupon bond that matures in 19 years if the market interest rate is 5.1 percent. Assume semiannual compounding.

Answer 1

Price of a zero-coupon bond is the present value of future cashflows discounted at required rate of return. As far as a zero-coupon bond is concerned, it does not pay any coupon payments, it pays only a lump sum amount on its maturity.

Value of zero-coupon bond = Face vale / (1+required return)^{time to maturity}

= 1000/(1+(.051/2))^(19*2)

= 1000/1.0255^38

= 1000/2.60348607269

= $384.10

note: When no face value is given, it is general practice to take $1,000 as face value.