NOMISMA
History's lessons for today's decisions / Calculate with Your Own Numbers

Calculating the amount lost to inflation

The amount on my pension notice has increased, but life isn't any easier. How much value is being lost?

How Much You Lose to Inflation in 3 Minutes

  1. See it
  2. In numbers
  3. What would you do?
  4. Read more

1See it

Swipe to see more

1 / 8

My pension payment has gone up, but life isn't getting any easier.

2 / 8

The face value is called the 'nominal' value.

3 / 8

The value after accounting for inflation is the 'real' value.

4 / 8

In 2025

In Japan, consumer prices (overall) rose 3.2% from the year before.

3.2%

5 / 8

If inflation is 2% a year, a nominal value of 100 becomes 82 in 10 years.

100 → 82

6 / 8

Loss in value = Nominal value − Real value

7 / 8

Use your annual pension amount or the amount in your fixed deposit.

8 / 8

This is a hypothetical calculation, assuming the rate continues. It doesn't predict future rates.

2In numbers

82

The real value of a nominal 100 after 10 years with 2% annual inflation.

Now100
10 years later82

3.2%

Increase in Japan's consumer price index (overall) in 2025.

3What would you do?

You've received a notice that your fixed deposit has matured. The face value is higher than what you originally deposited. How should you view this?

Pick one

Be relieved because it has increased.

Even if the face value (nominal value) has increased, the real value is a different number after accounting for inflation. You can convert it to today's value by dividing the face value by (1 + inflation rate) raised to the power of the number of years.

Account for inflation to see the real value.

That's right. For the inflation rate, use the consumer price increase from the most recent year. This is a hypothetical calculation based on the assumption that this rate will continue.

4Read more

Read the full story ↓

When to use When you receive your pension amount notice. When you receive a notice of your fixed deposit's maturity. When you see news of price hikes.

Face value and what it can buy

The face value amount is called the nominal value, and the amount after subtracting for inflation is called the real value. If prices rise by r percent per year, what the same face value can buy in n years will be today's value of 1 ÷ (1 + r/100) to the power of n. In 2025, Japan's Consumer Price Index (General) was a 3.2 percent increase from the previous year.

Formula

Real value = Face value ÷ (1 + inflation rate/100) to the power of number of years. Loss in value = Face value - Real value. If inflation is 2 percent per year, a face value of 100 becomes 82 in 10 years (100 ÷ 1.02 to the power of 10).

How to use

For face value, enter your annual pension amount or fixed deposit amount. For the inflation rate, enter the consumer price increase rate for the most recent year. Since the rate changes every year, this calculation is a hypothetical one based on "if that rate were to continue." It is not a prediction of future rates.

Where to check

Japan's Consumer Price Index is published monthly by the Statistics Bureau of the Ministry of Internal Affairs and Communications. In the U.S., the Bureau of Labor Statistics, and in the Eurozone, Eurostat, publish indices of the same form. If you substitute the rate, the formula is the same.

Try with your own numbers

If you change the numbers, it recalculates on the spot. The formula is written below.

Input value

Output value

Present value of what the same face value can buy in n years(Yen)—
Amount of value lost(Yen)—
Percentage of present value(%)—

Formula Dividing the face value by "1 + inflation rate" to the power of the number of years gives the amount converted to present value. The difference between the face value and that amount is the loss in value.

In other countries

The principle is common. The CPI from the U.S. Bureau of Labor Statistics and the Eurozone's HICP (approx. 700 items) are also indices of the same form, comparing the price of a basket of goods purchased by households with the previous year. You can calculate the loss in value with the same formula by substituting the rate. Both the Bank of Japan and the European Central Bank have set a 2 percent inflation target.

Bibliography

Related Lectures and Notes

P3 P4 P2

Back to "Everyday Money: Calculations and Procedures" list

Price

After purchase, the full courses, the illustrated books, every country’s story and the numismatics examination are open to you.

See the price →