Question

In January 2020, the term-structure of spot rates is as follows (with continuous compounding):

Maturity (years) Zero-rate(%)

1 2.0

2 3.0

3 4.0

A 3-year zero-coupon bond has the face value of $1,000. Consider a 1-year forward contract on the zero coupon bond. What should be the forward price?

(a) $904.84 (b) $923.12 (c) $941.77 (d) $960.79

Answer 1

Present value = Future value / e^n*r

n = number if periods

r = rate of interest

Step - 1:

First let's calculate spot value (i.e., at year 0)

Present value = 1000 / e^3*4%

= 1000 * 0.88692

Spot value = $886.92

Step - 2:

Future value = Present value * e^r*n

Value after one year = 886.92*e^1*2%

= 886.92 * 1.02020134

So forward rate = $904.84

Option a is correct