Question

Asked Jul 17, 2019

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Step 1

If r_{n} andrS_{n+1} are the spot rates for the year n and n+1 respectively, then one year forward rate between year n and n+1 is given by f_{n, n+1} and governed by the following equation:

(1 + r_{n})^{n} x (1 + f_{n, n+1}) = (1 + r_{n + 1})^{n + 1}

Step 2

In order to get f_{2, 3} we need to put n = 2. In that case, the equation becomes:

(1 + r_{2})^{2} x (1 + f_{2, 3}) = (1 + r_{3})^{3}

Or, (1 + 4.5%)^{2} x (1 + f_{2, 3}) = (1 + 5.5%)^{3}

Or, f_{2, 3} = (1 + 5.5%)^{3} / (1+ 4.5%)^{2} – 1 = 7.5288%

Step 3

In order to get f3, 4 we need to put n = 3. In that case, the equation becomes:

(1 + r3)3 x (1 + f3, 4) = (1 + r4)4

Or, (1 + 5.5%)3 x (1 + f3, 4) = (1 + 7%)4

Or, f3, ...

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