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# Money Inflation Calculator + Online Solver With Free Steps

The **Money Inflation Calculator** determines the current price of a product and the average inflation rate relative to a given base price and period.

## What Is the Money Inflation Calculator?

**The Money Inflation Calculator is an online tool that calculates the average inflation rate and the current price of a product that cost a known amount during some earlier period. **

The earlier time period is called the **base period**, and the price during it is called the **base price**. The current-year price is called the **updated/current price**.

Inflation is inherently between two different time instances. In this calculator, one of the time instances is the current day, and inflation is measured w.r.t. some earlier year (base period). You need to enter the base period and the base price.

For example, the price of bread today (2022) is not the same as in 1900. So 1900 is our base period, and 2022 is the current year. Inflation occurs in between.

The **calculator interface** consists of two descriptively labeled text boxes. The labels are self-explanatory. In the **first (top) text box**, you enter the price of a specific product in the base period **(the base price)**, and in the **second (bottom) box**, you enter the year corresponding to that price **(the** **base period)**.

In summary, the calculator takes information about the earlier year (base period) to calculate the updated price of that product in the current day.

## How To Use the Money Inflation Calculator

You can use the **Money Inflation Calculator** to find the current price of a product if you know the price from an earlier year. For example, if a digital piano cost 500 USD in 2015, you can get its current price from the calculator. Follow the step-by-step guidelines below for help.

### Step 1

Enter the base/old price of the product in the first text box. For the above example, we have $500, so we enter “500” here.

### Step 2

Enter the base period (year) during which the product had the base price. For our example, this is the year 2015, so we enter “2015.”

### Step 3

Press the **Submit** button to get the results.

### Results

The results appear as an extension to the calculator interface and consist of various sections:

**Input Interpretation:**Displays the user input as interpreted by the calculator. You can use it for manual verification.**Result:**The current-year price estimate of the product in the market. The calculator finds this using the known CPIs.**History: T**his shows a graph depicting the history of the product’s price. It starts from the base year and ends in the current year. Price is on the y-axis, and the years are on the x-axis.**Average Rate of Inflation:**This is the average inflation rate starting from the base year to the current year – measured as in equation (3).**Total Inflation Factor:**The ratio of the calculated current price to the base price. In other words, how much has the cost increased relative to the base price?

For our example, the results except for **History** are:

- Input Interpretation:
**$500**(2015 US dollars) in**2022** - Result:
**$567.88**(2022 US dollars) - Average Rate of Inflation:
**1.84% per year** - Total Inflation Factor:
**13.58%**

## How Does the Money Inflation Calculator Work?

The **Money Inflation Calculator **works by accessing the known **Consumer Price Index (CPI) **values for the base and current years. Then, it calculates the current year price as:

\[ \text{current price} = \text{base price} \times \frac{\text{CPI}_\text{current year}}{\text{CPI}_\text{base year}} \tag*{(1)} \]

### Consumer Price Index (CPI)

The Consumer Price Index is a standard method for measuring changes in product prices and, by extension, inflation. A record of annual CPIs is maintained by the **Bureau of Labor Services** (BLS) in the United States. Since 1913, BLS has tracked the price changes of around 94,000 products annually for CPI calculations. **The calculator has access to these values**.

With the CPI of the base year and the CPI of the current year, the following direct proportion applies:

\[ \frac{\text{current price}}{\text{base price}} = \frac{\text{CPI}_\text{current year}}{\text{CPI}_\text{base year}} \]

Rearranging the above equation gets us to the formula in equation (1).

Generally, equation (1) is used when CPIs are given relative to the base year. In such cases, the base year’s CPI is **normalized** to 100, and all other years’ CPIs are measured relative to it. If prices for some other year are lower relative to the base year, the CPI for that year is less than 100. Otherwise, it is greater than 100. If the prices remain the same, it is equal to 100.

Therefore, the CPI of 2022 relative to 2015 is **DIFFERENT** from the CPI of 2022 to 2014! While the calculator has access to the database and uses the normalized CPI values from there, it does not tell us the value of CPI used to calculate the current price.

### Finding CPI Given Current and Base Prices

A **general formulation** **to recover CPI** given the current and base prices exists. It may be required because the calculator does not show the used CPI value.

Let the CPI of the current year relative to the base year be $\text{CPI}_\text{current}’$, and the normalized (to 100) CPI for the base year be $\text{CPI}_\text{base}’ = 100$, then:

\[ \text{CPI}_\text{current}’ = \frac{\text{current price}}{\text{base price}} \times \text{CPI}_\text{base}’ \]

\[ \text{CPI}_\text{current}’ = \frac{\text{current price}}{\text{base price}} \times 100 \tag*{(2)} \]

### Average Rate of Inflation

Given the two prices, we can derive a formula for the **average rate of inflation** using the interest formula:

\[ C = P(1+i)^n \]

In this equation, within our context, i is an estimate of the average inflation rate, n is the number of years, P is the base price, and C is the current-year price. Then we can simplify this to get:

\[ \frac{C}{P} = (1+i)^n \]

\[ \sqrt[n]{\frac{C}{P}} = 1+i \]

\[ i = \sqrt[n]{\frac{C}{P}}-1 \tag*{(3)} \]

### Total Inflation Factor

We can now compute the **total inflation factor** as:

\[ \text{total inflation factor} = \frac{\text{current price}}{\text{base price}} \tag*{(4)} \]

The total inflation factor is simply the current year CPI $\text{CPI}_\text{current}’$ divided by 100.

## Solved Example

### Example 1

If a ream of paper costs **$3** in **1900**, what would be its cost in **2022** if the CPI of 2022 relative to the base CPI of 1900 is **3307**?

### Solution

Let us consider what we have:

**base price (ream of paper) = $3**

**base period (year) = 1900**

**current period (year) = 2022**

**CPI**$_\boldsymbol{\textsf{current}}’$** = 3307**

And since the current year CPI is relative to the base CPI, we can assume **CPI**$_\boldsymbol{\textsf{base}}’$** = 100**. Now we can use equation (1) to get the current price:

\[ \textsf{current price} = \mathsf{3} \textsf{ USD} \times \frac{\mathsf{3307}}{\mathsf{100}} \]

**current price = 99.21 USD = $99.21**

The average rate of inflation can be found using equation (3). The number of years **n = 2022 – 1900** **= 122**.

\[ \mathsf{i} = \sqrt[\mathsf{122}]{\frac{\mathsf{99.21} \textsf{ USD}}{\mathsf{3} \textsf{ USD}}}-\mathsf{1} \]

i $\approx$ 1.0291 – 1 = 0.0291

** i(%) **$\boldsymbol{\approx}$ **2.91%**