Economy

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.

Compound interest

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:

Elements of compound interest

The components or elements of compound interest are as follows:

How it is calculated

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

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:

Disadvantages

Some, though few disadvantages are the following:

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.

Written by Gabriela Briceño V.
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