When a person borrows money from some bank or financial institution, some extra amount is charged for using that money. This extra amount is called interest, and it can be charged in two ways: simple interest or compound interest.
In simple interest, interest is charged only on the amount borrowed, that is, the initial capital. In compound interest, interest is calculated on the amount borrowed plus the interest accrued in each period, that is, interest on interest.
| simple interest | compound interest | |
|---|---|---|
| Definition | Simple interest is interest calculated as a percentage of the initial principal amount. | Compound interest refers to interest calculated as a percentage of the starting principal plus accrued interest. |
| accruals | Added to the initial capital at the end of the application. | Added to the capital at the end of each investment period, forming interest on interest. |
| Growth | Linear. | Exponential. |
| Formula | J = C. i. t | M = C (1+i) ᵑ |
| Use | This type of interest is most often used to collect financing, back taxes, credit purchases, etc. | This type of interest is most used by the financial system, and in various economic calculations. |
| Return | Low. | High. |
| Principal Capital Value | Constant. | It changes throughout the loan period. |
| Interest charged on top of | Initial capital. | Initial capital + accrued interest. |
Definition of Simple Interest
Simple Interest is interest charged as a percentage of the original amount borrowed (or initial principal) over the entire term of the loan. The value of the interest rate must be agreed between the parties.
A common example of the use of simple interest occurs in financing loans, where interest must be paid only on the original amount that was borrowed.
The formula used to calculate simple interest is:
Simple interest = C × i × t
C = Initial Capital (or principal)
i = Interest rate
t = Time
Example of Simple Interest
If you borrow $1000 from your friend at an interest rate of 10% per year, over a period of 3 years, the amount of interest charged will be $300.
J = C × i × t
J = 1000 x 0.10 x 3
J = 300
In this case, R$ 1000 is the Initial Capital value and R$ 300 is the amount you will pay in interest, for having kept that money for 3 years. The amount you must return to your friend at the end of the 3rd year is called the Amount, which is the sum of the Initial Capital plus Interest. In this case, the amount will be R$ 1300.
The greater the Initial Capital and the time, the greater the interest.
Definition of Compound Interest
Compound interest is interest calculated as a percentage of the original principal plus accrued interest from prior periods.
In this method, we add the interest earned in the previous years to the initial capital, thus increasing the value of this principal capital. The interest for the next periods will then be charged on top of this new amount. Thus, interest rates grow exponentially.
The time interval between two interest payment periods is known as the conversion period, and at the end of each conversion period, interest is recalculated. Typically, banks calculate interest on a semi-annual basis, while financial institutions have a policy of calculating interest on a quarterly basis.
To calculate compound interest, use the following formula:
S = C (1+i) ᵑ
M = Amount
C = Initial Capital
i = interest rate per period
n = number of periods in which the initial capital was applied
Compound interest example
To demonstrate, let's assume you borrow $500,000 for three years from your friend, who charges a compound interest rate of 5% per annum, with the full loan amount and interest payable after three years.
In this case, interest will be calculated on the initial principal plus accrued interest. Calculating each year separately, the calculation would be as follows:
After the first year, interest payable would be $25,000 ($500,000 x 5% x 1).
After the second year, interest payable would be BRL 26,250 (BRL 525,000 (loan principal + first year interest) x 5% x 1).
After the third year, the interest payable would be BRL 27,562.50 (BRL 551,250 (loan principal + interest for the first and second year) x 5% x 1).
So, the interest payable after the 3 years would be BRL 78,812.50 (BRL 25,000 + BRL 26,250 + BRL 27,562.50), while the final amount would be BRL 578,812.50.
But instead of calculating the interest for each year separately, you can easily calculate the total interest payable using the compound interest formula:
M = C (1+i) ᵑ
M = BRL 500,000 (1 + 0.05) ³
M = BRL 500,000 [1,157625 - 1]
M = BRL 78,812.50
Now see the difference between:
- Profit and Revenue
- Active and passive
