Suppose that the risk-free yield curve is flat at $8 \%$ (with continuous compounding). The payoff from a derivative occurs in 4 years. It is equal to the 5 -year rate minus the 2 -year rate at this time, applied to a principal of $$\$ 100$$ with both rates being continuously compounded. (The payoff can be positive or negative.) Calculate the value of the derivative. Assume that the volatility for all rates is $25 \%$. What difference does it make if the payoff occurs in 5 years instead of 4 years? Assume all rates are perfectly correlated.