# Compound Interest | Formula and Examples # Compound Interest

So compound interest is interest earned on interest. When you add the earned interest back into your principal balance, which then earns you even more interest, compounding your returns.

##### We speak of compound interest when the sum taken into account for the compound interest calculation includes both:
• The capital (the amount of money initially invested).
• Interest accrued over previous periods
Interest earned in one period in turn generates interest in subsequent periods.

The interest is said to be “capitalised”.

This type of interest is mainly calculated and used when depositing money into a savings account.

Calculate how much an investment can earn you over time with compound interest.

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#### How compound interest works

Unlike simple interest, calculated on the unchanged basis of the capital, compound interest is a formula in which the sum taken into account for the calculation of interest includes previous interest, that which has been accumulated in previous years.

We also speak of capitalized interest: each year, the capital taken into account is inflated by the interest generated, which means that the more time passes, the more the interest grows. The duration of the investment is therefore essential, because the interest being gradually transformed into capital, it becomes more and more important over time.

Bonds, time deposit, high interest saving account, certificate of deposit (CD), works on this principle. Let’s say you invest \$10,000 on it, with an annual return of 0.75%:

• At the end of the first year, you will receive \$75 in interest (10,000 x 0.75).
• At the end of the second year, the capital was added to the interest of the previous year, so \$10,075; you will receive \$75.56 (10,075 x 0.75).
• At the end of the third year, you will receive €76.13 (10,150.56 x 0.75).

#### The calculation formula for compound interest

The calculation is more complex than in the context of simple interest.

##### To calculate compound interest over long periods, we use the following formula:

C0 (1+i)n = Cn

Does this remind you of the dark hours of your math lessons? Do not panic, this convoluted formula is actually not very bad.

C0 corresponds to the amount of the initial capital, the one you initially place in the financial product, the parenthesis (1 + i) refers to a year with the interest provided according to the remuneration, and the “power n” is none other than the number of years the placement lasts. Finally, Cn is the sum obtained at the end.

If we take the example of the \$10,000 deposited in the Certificate of Deposit or Time Deposit account, and we want to calculate the amount of compound interest over 5 years, this therefore gives:

10,000 x (1+0.0075)5 = 10,380.67

That is \$380.67 of interest received over 5 years.

Now you know how to calculate compound interest!

#### The impact of starting early is huge

The impact of starting as soon as possible is enormous, even with small sums.

For example: Save \$100 per month and place it at 4% per year

You’ll get \$14,000 after 10 years
You’ll get \$50,000 after 25 years

##### Another example

If \$ 1,000,000 (one million) is invested in a time deposit with an interest of 5% a year (because of the illustration, interest is considered annual, not monthly). Every time there is interest, the interest yield becomes the next principal. Calculate the return on investment deposits from the 1st to the 5th year!

The return on deposit investment will be like this:

• 1st year: \$ 1,000,000 + \$ 50,000 = \$ 1,050,000
• 2nd year: \$ 1,050,000 + \$ 52,500 = IDR 1,102,500
• 3rd year: \$ 1,102,500 + \$ 55,125 = \$ 1,157,625
• 4th year: \$1,157,625 + \$57,881.25 = \$1,215,506.25
• 5th year: \$ 1,215,506.25 + \$ 60,775,3125 = \$ 1,276,281,5625 (27.63% accumulation in 5 years)

If the deposit interest rate is 10%, then in 5 years the \$ 1,000,000 money will be \$ 1,610,510 (61.05% accumulation in 5 years)
If the deposit interest rate is 20%, then in 5 years the \$ 1,000,000 money will be worth \$ 2,488,320 (accumulated 148.83% in 5 years)

The greater the percentage of acquisition, the greater the effect of compound interest. A similar effect is also obtained from the length of time you invest, the longer the acquisition, the more powerful it will be.

##### It has positive and negative impacts

What people often forget is that the effect of compound interest in addition to being positive, it also has an impact on negative investment returns. The effect of compound interest in a positive direction is obvious.

The negative impact example is inflation, or also if the investment suffers a continuous loss, the result will be affected too. If inflation is getting bigger, the effect of tiered interest in the long term will also be bigger.

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