# Compound interest and inflation

## How to calculate compound interest and inflation (and how they affect each other)

Compound interest always sounds good but in reality there are always factors working against you. In a normal savings account, the compound interest earned will be less than the rate of inflation meaning that the effective interest rate is negative, i.e. your savings lose value over time. In currency trading, the interest you might earn on the currency you’re going long on will be offset by the interest you’ll have to pay on the currency you’re shorting.

The calculator below will show you what becomes of S (your starting amount) and regular deposits A for which the interest rate i is applied over n periods assuming A is added at the beginning of the 2nd and subsequent periods.

Use a positive rate to calculate the result of compound interest earned or use a negative one to show the result of inflation or compound interest charged. Use the difference to show the net result of both.

DescriptionDataMath
Start:$S$
Deposit:$A$
Rate %:$i$
Periods:$n$
Result:$X$

### Examples

1. Inflation only: \$1,000, at an annual rate of inflation of 2% (“-2” in the calculator), after 10 years, will buy what only \$817.07 buys today.
2. Inflation vs lump sum: If you put \$1,000 into a savings account at 1% vs 2% inflation, the effective rate is -1% and after 10 years it will be worth \$904.38.
3. Regular savings: If you save \$1,000 every month at 6% compounded every month (0.5% per month) you’ll have over \$1 million after 30 years. But is that interest rate reasonable? Also, this ignores inflation completely.

### Math: How to calculate the Result, X

If you start with S dollars, after one period (such as a month or a year), you’ll have S × i, where i is the periodic (monthly or annual) interest rate (remember that if expressed as a percentage, the value used for calculation is divided by 100). If you deposit an additional A dollars at the beginning of the next period, you’ll end that period with the previous total plus A all multiplied again by i and so on:

$X=\text{(}S\text{(}1+i\text{)}+A\text{)}×\text{(}1+i\text{)}$
$X=\text{(}\text{(}S\text{(}1+i\text{)}+A\text{)}×\text{(}1+i\text{)}+A\text{)}×\text{(}1+i\text{)}$
etc.

This can be generalized over n equal periods to arrive at this formula:

$X=S\text{(}1+i{\text{)}}^{n}+A\frac{\text{(}1+i{\text{)}}^{n}-1-i}{i}$

Allowing for the special case of X = S + An when i = 0.

### Caveats

For a given interest rate, more frequent compounding pays more interest. For example, \$1,000 at an annual rate of 12% compounded once at the end of the year pays \$120, whereas compounding 1% per month each month pays \$126.83.

This calculator isn’t going to be much use in the real world because interest rates vary and are normally calculated daily. Also, deposits are normally made monthly and months are not equal periods.

Also, consider where interest comes from. It’s paid because the money can be lent out at a higher rate or invested in a way that earns a net profit. You might be missing out on a better return.

“Compound Interest” at investopedia.com.

“Annual Percentage Rate - APR” at investopedia.com.

“Compound Interest Isn’t What It’s Cracked Up to Be” at money.usnews.com.

“The Drawbacks of Compound Interest” at blogs.cfainstitute.org.