Question

A bank loan department is trying to determine the correct rate for a 2−yr loan to be made two years from now. If current zero rates are 1−yr=2%,2−yr=3%,3−yr=3.5%,4−yr=4.5%, the foward rate for the loan should be?

Answer 1

The forward rate for a 2-year loan commencing in two years, given the zero rates of 3% for 2 years and 4.5% for 4 years, would be approximately 6.09% after solving the forward rate formula.

Step-by-step explanation:

To calculate the forward rate that should be applied to a 2-year loan beginning two years from now, we will use the current zero rates provided. The formula for a forward rate (F) starting two years from now (assuming semiannual compounding) for a two-year loan (from years 2 to 4) is (1 + z_{2})^{2} imes (1 + F)^{2} = (1 + z_{4})^{4}, where z_{2} is the 2-year zero rate and z_{4} is the 4-year zero rate.The forward rate for the loan can be determined using the concept of forward rates and the given zero rates. A forward rate represents the interest rate for a loan to be made in the future. In this case, the bank loan department is trying to determine the forward rate for a 2-year loan to be made two years from now.

Given z_{2} = 3% and z_{4} = 4.5%, the calculation would be as follows: (1 + 0.03)^{2} imes (1 + F)^{2} = (1 + 0.045)^{4}. Solving for F, we find that the 2-year forward rate for a loan starting in two years is approximately 6.09%.