Question 14.1: Suppose a professional golfer wants to invest some recent go...

If Inflation Is 2% a Year
The bank is paying a market rate (i ). The inflation rate (f) is given. What, then, is the real interest rate (i′)?

i = 5.5%           f = 2%           i′ = ?

Solving for i’ in Equation 14-1, we have

1 + i = (1 + i′)(1 + f) or       ;         = i′ + f+ i′f         (14-1)

i = i′ + f + (i′)(f)

i -f = i′(1 + f)

i’ = (i -f)/(1 + f)

= (0.055 – 0.02)/(1 + 0.02)

=0.034        or      3.4%  per year

This means that the golfer will have 3.4%  more purchasing power than she had a year ago. At the end of the year she can buy  3.4%  more goods and services than she could have at the beginning of the year. For example, assume she was buying golf balls that cost  $5  each and that she had invested $1,000.  At the beginning of the year she could buy

Number of balls purchased today =\frac{\text{Dollars today available to buy balls}}{\text{Cost of balls today}}

At the end of the year she could buy

Number of balls bought at end of year =\frac{\text{Dollars available at end of year}}{\text{Cost per ball at end of year}}

=\frac{(\$1,000)(F/P, 5.5\%, 1) }{(\$5)(1 + 0.02)^{1} }

=\frac{\$1,055 }{\$5.10}=207 golf balls

The golfer can, after one year, buy  3.4% more golf balls than she could before. With rounding, this is 207 balls.

If Inflation Is 8%
Again, we would solve for i′:

i′ = (i -f)/(1 + f)
= (0.055 – 0.08)/(1 + 0.08)
=  -0.023      or        -2.3% per year

In this case we can see that the real growth in money has decreased by 2.3%, so the golfer can now buy 2.3% fewer balls with the money she had invested. Even though she has more money at the end of the year, it is worth less, so she can buy less.

Regardless of how inflation behaves over the year, the bank will pay the golfer $1,055 at the end of the year. However, as we have seen, inflation can greatly affect the “real” growth of dollars over time.