The 1-year forward rate 2 years from now is calculated as:

$\text{Forward Rate} = \text{Spot Rate}_{\text{year 3}} + (\text{Spot Rate}_{\text{year 3}} - \text{Spot Rate}_{\text{year 2}}) \times \left( \frac{\text{Time}_2}{\text{Time}_3 - \text{Time}_2} \right)$

$\text{Forward Rate} = 0.072 + (0.072 - 0.065) \times \left( \frac{2}{3 - 2} \right) = 0.086 \text{ or } 8.6\%$

Alternative Approach

Let's start off by assuming that there are two people, each with $100.

• A chooses to invest his cash for 3 years straight at the 3-year spot rate.
• B opts to invest his cash for 2 years at the 2-year spot rate and then reinvest his proceeds for a further year at the 1-year forward rate at that point.

In a fair market, both A and B should have the same amount of money at the end of year 3. The 3-year spot rate is equal to the 2-year spot rate multiplied by the 1-year forward rate two years from today.

In other words:

$(1 + 3\text{-year spot})^3 = (1 + 2\text{-year spot})^2(1 + 1\text{-year forward})$

We should set the forward rate such that B ends with the same amount of money as A.

$`$1.07`2^3 = 1.065^2 \times 1\text{-year forward rate}$$

$`$1`\text{-year forward rate} = 0.086 = 8.6%$$