Using the given spot rates, the calculated forward rate for a one-year loan beginning in one year is 5%.
The forward rate for a one-year loan beginning in one year can be calculated using the given spot rates for three zero-coupon bonds: r(1)=3%, r(2)=4%, and r(3)=5%. The formula to determine the forward rate between year 1 and year 2 (denoted as f(1,2)) using spot rates is:
f(1,2) = [(1 + r(2))^2 / (1 + r(1))] - 1
Plugging in the given values, we have:
f(1,2) = [(1 + 0.04)^2 / (1 + 0.03)] - 1
This gives us:
f(1,2) = [(1.04)^2 / 1.03] - 1
f(1,2) = [1.0816 / 1.03] - 1
f(1,2) = 1.05 - 1
f(1,2) = 0.05 or 5%
Therefore, the forward rate for a one-year loan beginning in one year is 5%.