Independent solution

How to solve this Spot and Forward Rates question

Setup

Setup

Under a common annual rate, write each zero-coupon price as a discount factor.

P(0,m)=(1+i)−mP(0,m)=(1+i)^{-m}
P(0,n)=(1+i)−nP(0,n)=(1+i)^{-n}

Model

Model

One unit invested at time m grows for n minus m periods.

X=(1+i)n−mX=(1+i)^{n-m}

Compute

Compute

Divide the two zero prices to express that accumulation without the rate.

P(0,m)P(0,n)=(1+i)−m(1+i)−n=(1+i)n−m\frac{P(0,m)}{P(0,n)}=\frac{(1+i)^{-m}}{(1+i)^{-n}}=(1+i)^{n-m}

Answer

Answer

Therefore X equals P(0,m) divided by P(0,n), which is choice D.

X=P(0,m)P(0,n)(D)\boxed{X=\frac{P(0,m)}{P(0,n)}\quad\text{(D)}}