Compound interest

Compound interest is the accumulation of interest generated in a given period of time by an initial capital or principal at an interest rate during certain tax periods, so that, the interest earned at the end of the investment periods is not reinvested in the initial capital, i.e. capitalized.

Related topics

Simple interest, current value

What is compound interest?

It is the interest that is charged on a loan that, when liquidated, is added to the principal, which is why in the liquidation that continues, the first interest will become part of the principal of the new interest.

Characteristics of compound interest

The main characteristics of compound interest are as follows:

• The start capital changes in each of the periods because the interest is capitalized, which means that it becomes capital.
• The interest rate will always be applied on a different principal.
• Periodic interest is higher.
• Interest accrues plus interest.
• They can be applied in any type of operation, either short or long term.

Elements of compound interest

The components or elements of compound interest are as follows:

• Interest: this is the amount of money that is charged or paid for the use of the principal during a given time.
• The principal: this is the initial amount of money with which it starts, this money is borrowed or deposited plus the interest generated by previous periods.
• The rate: this is the amount of money that must be paid or charged per 100 for interest.
• Capitalization: this is the element that differentiates the compound interest and represents the number of times per year in which the interest will be reinvested.

How it is calculated

To know the compound interest, we must know a series of variables to consider in the calculation and these are:

• Present or current value: It is the current value of the credit or deposit and it is also called as initial capital.
• Interest or interest rate: It is the interest rate that will be charged or paid depending on the case.
• Period: It is the time or term during which the credit will be paid.
• Future value: The total value that will be paid at the end of the credit. It is also called final capital.

Formula

In reality, when we look for compound interest, we only need one formula and it is as follows:

VF = VP (1+i) n where VF is the Future Value, VP is the Present Value, i is the expired periodic interest rate and n is the number of periods or term.

Advantages

Some of the advantages of compound interest are as follows:

• All the interests are added to the money you had before, which is very good for the economy because it means that those interests also generate interests.
• The profits obtained at the end of each period are added to the initial capital and, for this reason, they cannot withdraw.
• The interest can be reinvested so that the savings grow quickly.

Disadvantages

Some, though few disadvantages are the following:

• The compound interest benefits cannot be seen before one year.
• Earnings depend on the product or service.
• Like money debts can increase.

How compound interest differs from simple interest

The difference between simple and compound interest is that the interest rate is simple when the interest we can obtain at maturity is not added to the principal in order to generate new interest through them. The simple interest will always have to be calculated on the initial capital. In this way, interests that are obtained are not reinvested in the following period and for this reason the interest obtained in each period will always be the same.

Compound interest, on the other hand, refers to the interests that we obtain in each period and that are added to the initial capital, creating new interests. In compound interest, unlike simple interest, interest is not paid according to its maturity, because it gradually accumulates to the principal. It is for this reason that the capital grows at the end of each of the periods and the interest calculated on a greater capital also grows.

It is also important to add that in simple interest the initial capital is the same throughout the operation, whereas in compound interest this capital will vary in each of the periods. In the simple interest the interest will always be the same, whereas in the compound interest the interest will vary.

In short, the main difference is whether or not the interests that are periodically caused are reinvested. With compound interest the interests are reinvested and for this reason we are able to obtain greater and better profits. Whereas, with simple interest, interest cannot be reinvested, and we always get the same amount.

Examples

Calculate the income of $30,000 deposited for the 3-year term with 10% annual interest, if at the end of each year the percentage was added to the money deposited.

Solution:

B = 30000 (1 + (10%/100%) )3 = 30000 · 1.13 = 39930

100%

Income equals

39930 – 30000 = 9930

Result: the income is $9930.