Final answer:
According to expectations theory, the two-year interest rate based on a first-year rate of 3% and an expected second-year rate of 5% would be approximately 4%, as it's the average of the two rates.
Step-by-step explanation:
The expectations theory suggests that the two-year interest rate can be determined based on the average of the current one-year interest rate and the expected one-year interest rate next year. If we have a one-year interest rate of 3% this year and it's expected to be 5% next year, the two-year rate would be calculated as the average of these two rates. This is done by adding the current year's rate (3%) with the next year's expected rate (5%) and then dividing by 2, which results in a 4% two-year interest rate.
To provide an example involving bond valuation, imagine that a local water company issued a $10,000 ten-year bond at an interest rate of 6%. If you are thinking about buying this bond one year before the end of the ten years, but interest rates are now 9%, you would expect to pay less than $10,000 for the bond due to the increased market interest rates. The exact price you would be willing to pay can be calculated by discounting the expected payments from the bond (which would be the final year's interest plus the principal repayment) at the new market interest rate of 9%.