Question

Consider the following spot interest rates for maturities of one, two, three, and four years.

            r₁ = 6.3%    r₂ = 7.1%     r₃ = 7.8%     r₄ = 8.6%

What are the following forward rates, where f_k,1 refers to a forward rate beginning in k years and extending for 1 year? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

f2, 1

f3, 1

Answer 1

(A) F2,1 is the forward rate of 1 year beginning at the end of year 2.

Let's suppose our investment value is $100.

If we invest it for 2 years, the future value will be : Formula : FV = PV*(1+rate)^years

Rate for 2 years spot is 7.1%

= $100*(1+7.1%)^2 =$114.70

If the same amount is invested for 3 years, rate of interest spot will be 7.8%

= $100 * (1+7.8%)^3 = $125.27

Amount changed from $114.70 to $125.27 in one year time from year 2 to year 3. Which means the return rate for this year would be : [Closing value/ opening value]-1 : [($125.27 / 114.70) - 1] = 9.21%

f2,1 = 9.21%

(B) F3,1 is the forward rate of 1 year beginning at the end of year 3.

Let's suppose our investment value is $100.

If we invest it for 3 years, the future value will be : Formula : FV = PV*(1+rate)^years

Rate for 3 years spot is 7.8%

= $100*(1+7.8%)^3 =$125.27

If the same amount is invested for 4 years, rate of interest spot will be 8.6%

= $100 * (1+8.6%)^4 = $139.10

Amount changed from $125.27 to $139.1 in one year time from year 3 to year 4. Which means the return rate for this year would be : [Closing value/ opening value]-1 : [($139.1 / 125.27) - 1] = 11.03%

f3,1 = 11.03%