Question

What is the one-year interest rate one year from now if the current one-year interest rate is 2.75% and the two-year interest rate is 3.21%? Assume the rates are effective annual rates. Multiple Choice 3.62% 3.67% 3.71% 3.75%

Answer 1

We need to use the concept of forward rate here formula for it is:

Forward Rate = [(1 + S₁)ⁿ₁ / (1 + S₂)ⁿ₂]^1/(n₁^-n₂⁾ – 1

One-year interest-rate one year from now is said to be F(1,1)

S₁ = Spot rate until a further future date = two-year interest rate = 3.21% = 0.0321

S₂ = Spot rate until a closer future date = one-year interest rate = 2.75% = 0.0275

n₁ = No. of years until a further future date = 2

n₂ = No. of years until a closer future date = 1

F(1,1) = [(1 + 0.0321)²/ (1 + 0.0275)¹]^1/(2-1) – 1

F(1,1) = [(1.0321)²/ (1.0275)]^1/1 – 1

F(1,1) = [1.06523041 / 1.0275] – 1

F(1,1) = 1.03672 – 1 = 0.03672 =3.67%

One-year interest rate one year from now is 3.67%