The 1-year, 2-year. 3-year, and 4-year risk-free zero rates are 4%, 4.5%, 4.75%, and 5% with continuous compounding. What is the forward rate for the one year period beginning in two years

5.25%

Explanation:

Mathematically, investing at the 3-year risk-free zero rate should be the same as investing at a 2-year risk-free zero rate and one-year forward rate beginning in two years as shown thus

(1+S3)^3=(1+S2)^2*(1+y2y1)^1

S3=4.75%

S2=4.5%

y2y1=unknown

(1+4.75%)^3=(1+4.5%)^2*(1+y2y1)

1+y2y1=(1+4.75%)^3/(1+4.5%)^2

y2y1=((1+4.75%)^3/(1+4.5%)^2)-1

y2y1=5.25%

odd consecutive integers are odd integers that follow each other. they have a difference of 2 between every two numbers. if n is an odd integer, then n, n+2, n+4 and n+6 will be odd consecutive integers. the first number in the pattern is always the variable on its own or in this case, "n". examples.