# Value of 2013 US Dollars today

\$100 in 2013

\$112.09 in 2020

The inflation rate in the United States between 2013 and today has been 12.09%, which translates into a total increase of \$12.09. This means that 100 dollars in 2013 are equivalent to 112.09 dollars in 2020. In other words, the purchasing power of \$100 in 2013 equals \$112.09 today. The average annual inflation rate has been 1.44%.

## Inflation timeline in the United States (2013-2020)

The following chart depicts the equivalence of \$100 throughout the years due to inflation and CPI changes. All values are equivalent in terms of purchasing power, which means that for each year the same goods or services could be bought with the indicated amount of money.

All calculations are performed in the local currency (USD) and using 6 decimal digits. Results show only up to 2 decimal digits to favour readability. Inflation data is provided by governments and international institutions on a monthly basis. Today's values were obtained by estimating figures from recent trends.

The following table contains relevant indicators:

Indicator Value
Total Inflation (2013-2020) 11.92%
Total Inflation* 12.09%
Annual inflation avg. (2013-2020) 1.62%
Annual inflation avg.* 1.44%
CPI 2013 96.87
CPI 2020 108.42
CPI today* 108.59
\$1 in 2013 \$1.12 in 2020

* Values extrapolated from the last official data to obtain today's values.

## How to calculate today's value of money after inflation?

There are several ways to calculate the time value of money. Depending on the data available, results can be obtained by using the compound interest formula or the Consumer Price Index (CPI) formula.

#### Using the compound interest formula

Given that money changes with time as a result of an inflation rate that acts as a compound interest, the following formula can be used: FV = PV (1 + i)n, where:

• FV: Future Value
• PV: Present Value
• i: Interest rate (inflation)
• n: Number of times the interest is compounded (i.e. # of years)

In this case, the future value represents the final amount obtained after applying the inflation rate to our initial value. In other words, it indicates how much are \$100 worth today. There are 7 years between 2013 and 2020 and the average inflation rate has been 1.4372%. Therefore, we can resolve the formula like this:

FV = PV (1 + i)n = \$100 * (1 + 0.01)7 = \$111.92

#### Using the CPI formula

When the CPI for both start and end years is known, the following formula can be used:

Final value = Initial value *
CPI final/CPI initial

In this case, the CPI in 2013 was 96.87 and the CPI today is 108.59. Therefore,

Final value = Initial value *
CPI final/CPI initial
= \$100 *
108.42/96.87
= \$111.92

### USA inflation - Conversion table

Initial Value Equivalent value
\$1 dollar in 2013 \$1.12 dollars today
\$5 dollars in 2013 \$5.6 dollars today
\$10 dollars in 2013 \$11.21 dollars today
\$50 dollars in 2013 \$56.05 dollars today
\$100 dollars in 2013 \$112.09 dollars today
\$500 dollars in 2013 \$560.46 dollars today
\$1,000 dollars in 2013 \$1,120.93 dollars today
\$5,000 dollars in 2013 \$5,604.63 dollars today
\$10,000 dollars in 2013 \$11,209.25 dollars today
\$50,000 dollars in 2013 \$56,046.26 dollars today
\$100,000 dollars in 2013 \$112,092.52 dollars today
\$500,000 dollars in 2013 \$560,462.61 dollars today
\$1,000,000 dollars in 2013 \$1,120,925.22 dollars today

Period Value
2013 100
2014 101.5
2015 102.27
2016 103.02
2017 105.15
2018 107.37
2019 109.42
2020 111.92
Today 112.09