Math: inflation and interest

Recalling the 70s and 80s, the math tutor proposes a nostalgic premise for your coffee break.

Inflation eats away at your money.  Right now, inflation is very low; it has been since the late 90s. However, in the 70s and 80s inflation was significant – and very high some years.

You can tell inflation is at work if prices are going up.  I remember chocolate bars, chips, and pop used to cost a quarter each when I was six.  A year later, they all cost 30 cents.

To calculate the inflation rate in the case above, we do this:

rate=(change in price)/(former price)

In our case


To change from a decimal to a percent we move the decimal point two jumps right:


Of course, 20% inflation is very high; I don’t imagine inflation is even 2% right now.

From what I’ve read, interest rates generally run around 3% above inflation. That’s a historical trend, so it may not be the case at any given time. However, if interest offered to savers is 6%, inflation is likely around 3%.

Let’s find the change in value of $1000 over a year at 6% interest with 3% inflation (we assume the $1000 is in a savings account):


The principal is the amount deposited in the account. Of course, the rate must be in decimal form. To go from percent to decimal, you shift the decimal point two places left (or else you can just divide by 100):


Now we can find the interest earned:


Before considering inflation, the $1000 has grown to $1060.

Now let’s witness the action of inflation. The real value of the $1060 at year end is as follows:

real value=(1-inflation rate)*dollar_amount

Once again, the inflation rate must be in decimal form. We realize that 3% is 0.03 and proceed:

real value=(1-0.03)*1060=0.97*1060=1028.20

So the proceeds are $28.20 after inflation.

In a future post I’ll mention a surprising twist about the relationship between inflation and interest:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

Leave a Reply