Simple and compound interest

Simple interest is that which is not added to the initial capital once the term of the investment or credit has expired.

Compound interest is that which is added to the initial capital at the end of the investment or credit.

The difference between simple interest and compound interest is that the simple one is not capitalizable, while the compound helps to increase the initial capital.

	Simple interest	Compound interest
Definition	The non-capitalizable interest rate has no impact on the initial amount of an investment.	It is an interest rate that is added to the capital at the expiration of the period, increasing the initial amount of the investment
Characteristics	It is calculated on the initial capital. Does not vary. Does not generate capital increase.	It is calculated on the final capital. Increases in each period. Generates capital increase.
Elements	Initial capital. Interest applied to capital. Weather. Interest paid.	Initial capital. Final capital. Interests. Weather.
Formula	I = C x i x t	Cf = Ci (1 + i) ᵗ

What is interest?

Before understanding the difference between simple and compound interest, it is important to know the concept of interest in the world of finance..

Interest is an amount of money that is generated in a period of time during which an investment, savings or loan is maintained. That is, it is the profitability produced by the initial capital. It is expressed in percentages and is calculated annually.

What is simple interest?

It is that interest that is calculated and paid on the initial capital during a certain period. Upon expiration of said period, the interest generated is not considered to be reinvested in the capital, so it remains the same.

In practice, this means that when the term of an investment, savings or loan expires, the interest generated is not considered capitalizable and (if the person or company so wishes) begins a new investment or credit period that will generate the same interest. on the same capital.

In the case of credits, simple interest only applies when the debtor pays said interest within the agreed period. Otherwise, compound interest begins to accrue.

Simple interest characteristics

Simple interest has three essential characteristics:

• The capital will not vary in the period that the operation lasts (30 days, 60 days, 90 days, etc.)
• Every time you start a new investment or credit period, the interest will remain the same.
• Interest is calculated and paid on the initial principal.

Elements of simple interest

To calculate simple interest, 4 components are required:

C: initial capital.

i: interest applied to the initial capital (expressed by dividing the interest rate by 100).

t: time or period of the investment or credit (expressed in years, months or days).

I: interest paid (or collected, if it is a credit) at the expiration of the period.

Formula for calculating simple interest

Knowing the elements that make up simple interest, it is possible to calculate how much it would generate on an initial capital in a given period. The formula to use would be the following:

I = C x i x t

The interest paid is equal to the initial capital, multiplied by the interest applied to said capital, times the investment time.

Simple interest calculation example

To calculate the interest paid that would be generated on a capital of 100,000 pesos at a rate of 5% during a period of 2 years, the formula would be applied as follows:

I = 100,000 x 0.05 x 2

I = 10,000

In a period of two years, and with an interest of 5%, a capital of 100,000 pesos would generate an interest paid (or profit) of 10,000 pesos.

What is the composed interest?

It is the interest that is generated on the capital once the time limit established for saving, investment or loan has been met, and that when said term expires, it becomes part of the initial capital.

This means that, in the case of investments or savings plans, the profits generated are added to the capital, and if a new period begins, the interest will be calculated on the basis of this new capital (previous capital plus the interest generated).

While in the case of loans or credits, the interest generated becomes part of the accumulated debt.

Characteristics of compound interest

Compound interest has 3 elements that define it:

• As interest is added to the capital in each period, it increases.
• The interests are increasing in each period.
• In each new investment or credit period, the interest is calculated based on the current capital.

Elements of compound interest

As in compound interest the final principal varies in each period, this must be considered in the calculation of the interest paid or profit. In this case, the elements for the calculation of the formula are the following:

Cf: final capital

Ci: initial capital

i: interest (expressed by dividing the interest rate by 100, and then dividing the result by 12 months).

t: time or period of the investment (expressed in years, months or days)

Compound interest formula

In the compound interest formula, the element time is represented exponentially.

Cf = Ci (1 + i) ᵗ

Compound interest calculation example

To calculate the interest paid that would be generated on a capital of 80,000 pesos at a rate of 15% during a period of 2 months, the formula would be applied as follows:

Cf = 80,000 (1 + 0.0125) ²

Cf = 82,012.5

In a period of two months of investment, the initial capital increased 2,012.5 pesos with a rate of 15%.

See also:

• Difference between cost and expense.
• Fixed and variable costs