Question

You want to decide whether to invest in zero-coupon bonds or not. Currently, the yield to maturity of these zero-coupon bonds for the one-year is 8% and for the two-year is 9%. Given this information what is the forward rate of interest for the second year?
a. 10.01%
b. 8%
c. 9.2%
d. 3.25%

Answer 1

Answer:

The forward rate of interest for the second year is;

a. 10.01%

Explanation:

Step 1: Determine the 1 year final value of the investment

The formula for calculating the final value for the 1 year investment is;

F.V=P.V(1+r)

where;

F.V=final value

P.V=present value

r=yield to maturity

In our case;

F.V=unknown

P.V=x

r=8%=8/100=0.08

replacing;

F.V=x(1+0.08)=1.08 x

Step 2: Determine the 2 year final value of the investment

Using the formula;

F.V=P.V(1+r)²

where;

F.V=unknown

P.V=x

r=9%=9/100=0.09

replacing;

F.V=x(1+0.09)²=1.1881 x

Step 3: Determine the forward rate of interest for the second year

The forward rate of interest can be expressed as;

forward rate of interest=(2-year future value/1-year future value)-1

replacing;

forward rate of interest=(1.1881 x/1.08 x)-1=0.10009×100=10.01%

forward rate of interest=10.01%