Consider the following annual spot interest rates for maturi…
Consider the following annual spot interest rates for maturities of one, two, three, and four years:r1=3.7%,r2=4.3%,r3=5.1%,r4=5.8%.r_1 = 3.7\%, \quad r_2 = 4.3\%, \quad r_3 = 5.1\%, \quad r_4 = 5.8\%.What are the following forward rates, where f1,kf_{1,k}denotes the forward rate for an investment that begins in one year and lasts for kkyears?a) f1,1=?f_{1,1} = ?b) f1,3=?f_{1,3} = ?Hint: Use the relationship between spot rates and forward rates:(1+r1) (1+f1,k)k=(1+rk+1)k+1.(1 + r_1)\,(1 + f_{1,k})^k = (1 + r_{k+1})^{k+1}.Show all steps used to obtain your answers.