Question

The 8-year spot interest rate is 5.86%, the 4-year spot rate is 4.71%. What is the forward rate you can find using the pure expectations theory? Round to the nearest 0.01%. E.g., if your answer is 5.78%, enter it as 5.78.

You invested in a one-year debt security and realized a pre-tax return of 4% for the year. You happen to be in the 16% tax bracket. Inflation during the year was 4.3%. What is your realized after-tax real return, in %, to the nearest 0.01%? E.g., if your answer is 2.254%, record it as 2.25.

Answer 1

Question 1:

By using pure expectation theory, we can find the 4-year interest rate 4 years from now

Let "r" represent the 4 year interest rate 4 years from now.

This can be calculated as : (1+0.0471)^4 *(1+r)^4 = (1+0.0586)^8

(1+r)^4 =(1.0586)^8/(1.0471)^4 = 1.3119

r = 0.07023 = 7.023%

4-year interest rate 4 years from now = 7.023%

Question 2:

After tax return = 4%*(1-0.16) = 3.36%

Real return after tax return= (Nominal - Inflation)/(1+ Inflation) = (0.0336-0.043)/(1+0.043) =-0.90%

Real after tax return = -0.90%(Negative)