Negative Interest Rates

Most financial calculators currently in production will allow the interest rate to be negative.  Some older calculators do not.  The following alternative procedures can be used instead.  (If your calculator can handle negative interest rates, you don't need these examples.  Just enter your numbers and compute the result.)

If you want to find the interest rate, switch the values of FV and PV and compute the (now positive) rate.  However, since percent increases and percent decreases have different bases, you need to invert the percent change.  See example 1.

If you want to use a negative interest rate, first find the percent increase which is the inverse of the percent decrease.  See example 2.

Example 1.

A house declined in value over 6 years from \$185,000 to \$162,300.  Find the annual rate of deflation.

The original variables are:

 N = 6 x 1 = 6 I = ??? PMT = 0 PV = 185000 FV = 162300

Changing the problem to find a percent increase, we have:

 N = 6 x 1 = 6 I = ??? PMT = 0 PV = 162300 FV = 185000

The answer to the percent increase problem is 2.21%.  To find the inverse of 2.21%, we set up a percent change diagram:

 100.00% Old 2.21% + Change 102.21% New 100%

This can be solved using proportions:

100.00 x 2.21 / 102.21 = 2.16

Therefore, the house experienced 2.16% annual deflation.

Example 2.

Calculator prices are dropping 4% per year.  If a calculator costs \$75 today, what will it cost in 5 years?

The original variables are:

 N = 5 x 1 = 5 I = 4 / 1 = 4 PMT = 0 PV = 75 FV = ???

To change the problem into a percent increase, we use a percent change diagram:

 100.00% Old 4.00% - Change 96.00% New 100%

This can be solved using proportions:

4 x 100 / 96 = 4.1666...

Therefore, the inverse of a 4% decrease is (approximately) a 4.17% increase.  (We will keep the unrounded figure to maintain accuracy.)

The new variables are:

 N = 5 x 1 = 5 I = 4.1666... / 1 = 4.1666... PMT = 0 PV = ??? FV = 75

Solving for PV, we get \$61.15.  After 5 years of 4% per year price decreases, the calculator will sell for \$61.15.