Compound interest

Compound Interest

In the simplest sense, compound interest involves earning (or owing) interest, not only on the starting capital, but also on the interest already raised on that capital. The interest is thus compounded.

Explanation

Whenever a lender lends a sum of money to another person or company, the lender typically asks interest. Interest makes it interesting for a lender to lend money. This is because the the total sum returned will be greater than what was lent. For example, if a bank lends $400.000 to someone to buy a house, it will ask them to return the sum including interest. If the bank would not ask interest at all, it cannot invest that $400.000 somewhere else and thus, the bank cannot grow profit during the repayment time. The bank may even effectively lose money because of inflation. Hence, to make the loan interesting for the lender, a percentage of the original sum is added over time.

In our example, the bank may lend $400.000 and wants you to repay it within 30 years with an interest of 4%. If the bank would not use compound interest, but regular interest, it would be repaid $400.000 * 1.04 = $416000 after thirty years. This may not even compensate for inflation. So, to make it more profitable for the bank, it asks you to pay the interest yearly over the sum that still needs to be repaid. If you would not repay anything, then in the first year the sum would have increased to $400.000 * 1.04 = $416.000. This is a difference of $16.000. However, the next year, that interest of 4% is not calculated over the original sum, but over the new sum. That is the sum over which the interest has already been calculated over once! Hence, the second year, without repayment, the new sum becomes $416.000 * 1.04 = $432.640, which is a difference of 16640. The next year, the sum becomes $449.945. In 10 years, the sum becomes $592.097. In 30 years, the sum becomes $1.297.359. See the image below to see the interest accrue over time.

Compound Interest

With regular interest, the value of $400.000 would become only $416.000 after 30 years. With compound interest, this value was raised to $1.297.359.

Now you see how compound interest is a very useful way to generate revenue by only waiting. This is usually what people mean when they advice to make money work for you.

Formula

To calculate compound interest, the following formula is used:

• A = Final amount.
• P = The initial amount, also called principal.
• r = Interest rate
• n = Number of times interest is compounded per year
• t = Time in years

This formula does not take into account monthly contributions by withdrawing or depositing money.