Introduction: Banks don’t give away loans for free to their customers. They charge an additional amount in return which is called the interest. Every year there is a fixed rate according to which this interest gets added. One such simple way to calculate this is the simple interest method. Here the calculation is simple as the interest is constant every year. In some cases, the interest also increases each year for the same principal value. Banks refer to this process as the compound interest. The amount that you will get from this process is more than the simple interest.
The idea of compound interest: It is very easy to understand compound interest if you know the simple one. The only difference between the two is that the interest increases. You have to do the calculations individually to get the final answer. Foor 1st year you need to calculate the interest in the same formula (PTR/100). After that, you will get a definite value of interest. Add it with the principal to get the amount generated in that year. Then for the next year, the principal will be this amount only. This is the most crucial step that kids need to do in compound interest. You need to continue this process until you complete the number of years in the question.
The formula for compound interest:
The process of deriving the formula is based on the above concepts. First, you need to calculate the amount for one year. If you take the principal as “P” then the amount will be P + PR/100. The time here is just one and thus you can take the P outside as well. Then, the Amount for one year can be abbreviated as P(1+ R/100). Now for the consecutive years, the term (1 + R/100) will just get multiplied. Hence you have to take the time as the power of this term. The universal formulae for Amount in the compound interest chapter are P(1 + R/100) ^ t. Even if the time is given in months you have to convert it into year form.
For the half-yearly and quarterly process: In these situations, the time for the formula just changes. You have to focus on the “n” part of the formula. There are changes in the rate of the equation as well. You have to divide it by two as the year is half. This slight change will give you a completely different answer. Depending on the division you have to make changes to both the rate and the time. Changing just one aspect will not give you the correct answer. Similarly, for the quarterly time, you have to divide the rate by 4. The formula for compound interest will become P(1+R4100)4T−P.
Uses of compound interest
The rate of mortgage interest is calculated with this technique only. That is why its rate keeps on increasing if you see. In normal cases, simple interest is not used in most banks. They all use compound interest to find how much a customer owes them. There are some situations where the cash flow becomes compact in a business. They need loans to buy equipment and fix different parts. In such cases, the companies always go for a loan based on compound interest. Even in vehicle loans, the customer uses this process. The cars that you take will have a high interest by the time you pay money for them. Hence you need to know where the amount gets added after a year.
Compound interests are used in different fields of work in real life. Get a brief idea about the subject from math classes on the Cuemath website.