## What Is Compound Interest?

To understand the compound interest (or compounding interest) and its difference from the simple interest, we first need to summarize how the simple interest is calculated.

Simple interest is for each interest period calculated as interest from the principal.

On the contrary, compound interest is interest calculated on the initial principal, which also includes all of the accumulated interest from previous periods. In short, **compound interest takes into account also the interest on interest**.

## Why Is Compound Interest So Important?

Albert Einstein told following about compound interest: “**the eighth wonder of the world. He who understands it, earns it … he who doesn’t … pays it**“.

Warren Buffet had called it **the single most powerful factor behind his investing success**. He started investing at 11 years old. However, 99% of the wealth he earned after his 50th birthday.

### What is it that makes compound interest so powerful?

Compound interest carries a simple, yet a mind-blowing idea. The idea is that the interest is calculated also from the already accrued interests.

Let me show it in the following example: Let’s say we put $100,000 on a savings account with an annual interest rate of 5%. I put the numbers into our Compound Interest Calculator above, and this is the results summary.

Year | Amount - start of the year | Interest per year | Total interest | Amount - end of the year |
---|---|---|---|---|

1 | $100,000.00 | $5,000.00 | $5,000.00 | $105,000.00 |

2 | $105,000.00 | $5,250.00 | $10,250.00 | $110,250.00 |

3 | $110,250.00 | $5,512.50 | $15,762.50 | $115,762.50 |

... | ... | ... | ... | ... |

20 | $252,695.02 | $12,634.75 | $165,329.77 | $265,329.77 |

As you can see, the interest in the first year is $5,000. For the second year, it is already $5.250. For the third year, it will be $5,512.5. And for the 20th year, it will be $12,634.75. (Use the calculator on the top of this page to check the complete calculation.)

How is it possible that the interest in the 20th year of saving is more than 2.5 times larger than in the first year? The answer is compounding. **Compounding is a very powerful tool.**

## How is compound interest calculated?

Compound interest calculation can be a simple but also relatively complex matter. It depends on what factors we want to take into account. The simplest calculation is with one initial deposit and a fixed annual return (interest rate) for the entire interest period. In this case, the following formula will be used for the calculation.

where:

– the future value of an investment

– the principal investment amount (initial deposit or loan)

– the interest rate (decimal) (eventually the inflation rate)

– the frequency of compounding (the number of times that interest is compounded per period)

– the number of periods the money is invested for

Explanation of and can be confusing, so let’s explain it a bit further. If we compound once a year and the year is our base unit of time, then both variables will be equal to 1. If we compound monthly and our base unit is again a year, then will be equal to 12 while will be equal to 1.

From the above compound interest formula, formulas for calculation of time, interest rate, or initial deposit can be derived. If you are interested in these formulas and their explanations, let me know, and I will add them to the article. However, I do not currently consider it necessary.

## How to calculate compound interest with regular deposit or withdrawal?

A significantly more complex problem is the calculation of compound interest with regular deposits or withdrawals that take place during the saving/investment period. Since the principal, which bears interest, changes to us, so to speak, due to deposits (or withdrawals), the calculation is more challenging.

When calculating compound interest, it also depends on whether we want to attribute the deposit/withdrawal at the beginning or end of the interest period. Another variable is the ratio between the interest rate and the deposit/withdrawal frequency. Simply put, there are quite a few variables that affect the final calculation.

Such a calculation consists of two elements. The first is the compound interest for the initial deposit, and the second is the future value of a series of regular deposits or withdrawals. Below I will give a formula that takes into account the attribution of a regular payment (deposit or withdrawal) always at the end of the payment period. It will be quite complex, and I will describe only what the individual variables mean.

where:

– final amount/future value of an investment

– principal (initial amount)

– amount per period – an amount (deposit or withdrawal) attributed always at the end of the period

– annual interest rate (eventually expected annual return on investment, or annual inflation rate)

– number of interest periods in 1 year

– number of installments/payment periods in 1 year

– duration of the investment

– interest rate for 1 payment period/installment

– total number of installments/payment periods

## The longer the investment, the bigger the effect of compounding

The effect of compounding is getting stronger with every new compounding period. Try to play a bit with the compounding calculator on the top of this page. Check how large the effect of compounding is when you chose 10 years investment horizon, 30 years, and for example, 50 or 60 years. There is only one advice from me to you: **Start with your saving or investment today. Each day counts.**

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