Suppose you are investing in a bond and you want a real retu

Suppose you are investing in a bond, and you want a real return of 10% per year. You believe that the ination rate will be 3% per year over the lifetime of the bond. Using the Fisher equation, calculate the exact nominal interest rate at which you would be willing to lend. Using the approximate Fisher equation, calculate the approximate nominal rate at which you would be willing to lend. Comment on thedierence in your answers. (Hint: is the dierence substantial? When would we prefer to use the exact vs. the approximate formula?)

Solution

(a) Using Exact Fisher equation,

(1 + Nominal rate) = (1 + Real rate) x (1 + inflation rate)

= 1.1 x 1.03

= 1.133

Nominal rate = 1.133 - 1 = 0.133, or 13.3%

(b) Using approximation,

Nominal rate = Real rate + Inflation rate

= 10% + 3%

= 13%

(c) There is a difference of 0.3% only which is very small.

This difference will be considered significant (and exact formula should be used) in two circumstances:

1. When we\'re discounting or compounding, using real rate, a huge sum of money (where the dollar difference will be significant), and/or

2. Compounding/discounting is done for multiple period. The more the number of periods, the higher this difference.