Future Interest Rate Calculator based on Expecation Theory Notes
Current Interest Rate for N Years (%) (R) The annual rate of return for N years, such as 5(%)
Current Interest Rate for M Years (%) (r)  The annual rate of return for M years, N>M, such as 5(%)
N Years N years
M Years M years, M<N
Interest Rate from Year M+1 to year N (actural number)(%) (x) (refer to the equation on the right) --

Based on the expectation theory, the interest rate for (N-M) years but starting from year M+1 should satisfy the following equation:

(1+R)^N = (1+r)^m *(1+x)^(N-M)

Interest Rate from Year M+1 to  year N (approximation) (%) (x) (refer to the equation on the right) --

Based on the simple version of the expection theory (arithematic version), the interest rate for (N-M) years staring from year M+1 should satisfy the following equation:

N*R = M*r +(N-M)*(x)

Notes:

What is the Expectations Theory

The expectations theory attempts to predict what short-term interest rates will be in the future based on current long-term interest rates. The theory suggests that an investor earns the same amount of interest by investing in two consecutive one-year bond investments versus investing in one two-year bond today. The expectations theory is also known as the Unbiased Expectations Theory.

Example of Calculating Expectations Theory

Let's say that the present bond market provides investors with a three-year bond that pays an interest rate of 20 percent while a one-year bond pays an interest rate of 18 percent. The expectations theory can be used to forecast the interest rate of a future two-year bond.

(1+20%)*(1+20%)*(1+20%) = (1+18%)*(1+x)*(1+x), so X = 21.01%

Or 20%+20%+20% = 18% + x+x, so x=21% (the arithematic version)

https://www.investopedia.com/terms/e/expectationstheory.asp

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