Calculation of compound interest: formula for capitalization of deposits

What is capitalization and how does it multiply capital

In the financial world, there are two main mechanisms for calculating profitability. If, when using simple interest, profit is accrued only on the starting amount, then compound interest (capitalization) work on the principle of “interest on interest”. This means that at the end of each billing period, the earned profit is not withdrawn to a separate account, but is added to the principal amount (deposit body).

In the next period, the bank charges interest on this increased amount. Thus, the basis for calculation is constantly growing, forming a snowball effect. The longer the money is in the account, the faster the final profit increases. The famous physicist Albert Einstein is often credited with the phrase:“Compound interest is the eighth wonder of the world. He who understands it earns it, he who does not understand pays it.”

Mathematical formula for calculations

To manually calculate the total (when income is added once a year), a basic algebraic formula with powers is used:

• S - the final amount that you will receive in your hands at the end of the term.
• P - starting capital (initial deposit amount).
• I - annual interest rate.
• N - the number of periods (in this case, years) for which the funds are placed.

Step-by-step example of calculation using real numbers

Let's say an investor places 100,000 rubles on a bank deposit for a period of 3 years with a rate of 10% per annum and annual capitalization.

1. Year 1. The bank charges 10% on the starting amount. The profit is 10,000 rubles. By the end of the first year, the account contains: 100,000 + 10,000 = 110,000 rubles.
2. Year 2. Now 10% is credited to the new base (RUB 110,000). The profit for the second year will be 11,000 rubles. Account amount: 110,000 + 11,000 = 121,000 rubles.
3. Year 3. In the last year, interest is accrued on RUB 121,000. Profit increases to 12,100 rubles. Total amount to be paid: 121,000 + 12,100 = 133,100 rubles.

For comparison: if the investor had chosen simple interest (without capitalization), he would have received exactly 10,000 rubles every year, and the total amount would have been 130,000 rubles. The difference of 3,100 rubles is the result of compound interest. And the longer the investment horizon, the more colossal this gap will be.

How does the frequency of accruals affect the final profitability

In banking agreements you can often find different payment terms: annually, quarterly, monthly or even daily. The mathematical rule here is strict: the more often capitalization occurs, the higher the final return on the investment.

If interest is added every month (frequency n=12), then the base capital begins to grow faster from the second month. With long-term planning (for 5, 10 or 20 years), a deposit with monthly capitalization will always outperform its counterpart with an annual payment, even if their nominal interest rates are exactly the same.