Economy# Compound interest

## What is compound interest?

## Characteristics of compound interest

## Elements of compound interest

## How it is calculated

## Formula

## Advantages

## Disadvantages

## How compound interest differs from simple interest

## Examples

**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

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.

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**.

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.

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.

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.

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.

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.

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.

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.

Written by Gabriela Briceño V.

Briceño V., Gabriela. (2019). *Compound interest*. Recovered on 23 February, 2024, de Euston96: https://www.euston96.com/en/compound-interest/