Question

Suppose the current, zero-coupon, yield curve for risk-free bonds is as follows:

Maturity (years) 1 2 3 4 5
Yield to Maturity 4.70% 5.20% 5.45% 5.65% 5.80%
(a) What is the price per $100 face value of a 3-year, zero-coupon risk-free bond?

Answer 1

The price per $100 face value of a 3-year, zero-coupon risk-free bond is $86.08.

Step-by-step explanation:

To calculate the price per $100 face value of a 3-year, zero-coupon risk-free bond, we need to use the yield-to-maturity from the zero-coupon yield curve.

First, we convert the yield-to-maturity to a decimal by dividing it by 100. The yield-to-maturity for a 3-year bond is 5.45%, so the decimal form is 0.0545.

To calculate the price, we use the formula: Price = Face Value / (1 + Yield)^Number of Periods. In this case, the Face Value is $100 and the Number of Periods is 3. Plugging in the values, we get: Price = 100 / (1 + 0.0545)^3 = 86.08.

Therefore, the price per $100 face value of a 3-year, zero-coupon risk-free bond is $86.08.