### What is Compound Interest?

Compound interest is calculated on the principal amount and this is the interest that is accumulated over time. Unlike simple interest where instead of adding value to the principal amount, interest is calculated for next few years. The major application of compound interest can be seen in our daily transactions and finance sector and other areas as well. For example, it is used to calculate increase or decrease in population, it is used to calculate the depreciation value of an item, it is used to check the growth of bacteria etc.

To calculate interest, there are two popular methods in mathematics. These are simple interest and the compound interest. The simple interest is the value calculated on principal amount where compound interest is the return value on principal amount plus interests previously gained by you. For example, if you invested $2000 and earned an interest of $ 100 then the new principal amount would be $2100. From the next time, interest would be calculated on the new principal amount, not the initial investment i.e. $2000.

## Compound Interest Formula

As discussed, Compound interest is the interest of interest to the principal sum of a deposit. The concept is based on the fact where interest is added back to the principal amount and next interest will be calculated on new principal value during the next compounding value.

Compound interest opens doors of profit for a Company. Here, investors generally earn higher profits than expectations. The profits can be reinvested in the business and it works as a return multiplier with each passing year. Next major application of compound interest is pension payments where consistent returns on investment are enjoyed for a plenty of years.

#### The compound interest formula can be written as –

\[\large Compound\;Interest=P\left ( 1+\frac{R}{100}\right)^{T} – P\]

Where,

P = Principal

R = Rate

T = Time

*Compound Interest can also be called as Amount (A)*

### Monthly Compound Interest Formula

The idea of compound interest seems interesting when you are earning an attractive financial balance on your investments. For credit card holders, the knowledge of compound interest will help them in calculating payments quickly. If you are a borrower then it is not so pleasing but if you are an investor, you will reap the benefits as money grows.

#### The formula for monthly compound interest could be given as –

\[\large Monthly\;Compound\;Interest=Principal\left ( 1+\frac{Rate}{12}\right)^{12 \times Time} – Principal\]

### Daily Compound Interest Formula

The interest that is calculated on the primary principal amount and also this is the accumulated interest over a period of deposits. In simple terms, compound interest is the “interest on interest”. Based on compound interest, loan grows faster when compared to simple interest. The amount of interest that is calculated on bank accounts on monthly or daily basis is named as the compound interest. The daily compound interest formula in mathematics could be written as given below.

#### The formula for Daily compound interest could be given as –

\[\large Daily\;Compound\;Interest=Principal\left ( 1+\frac{Rate}{365}\right)^{365 \times Time} – Principal\]

The concept has a plenty of application in our day to day life. A depth understanding of the concept always makes you a better resource in resolving the issues around you related to the mathematics.

**Question 1: **A sum of Rs 4000 is borrowed, and the rate is 6%. What is the daily compound interest for 2 years?

** Solution: **

Daily Compound Interest = Principal\[\large (1+\frac{Rate}{365})^{365*Time}\] – Principal

Daily Compound Interest = 4000\[\large (1+\frac{6}{100*365})^{2*365}\] – 4000

Daily Compound Interest = 4000 * 1.127 – 4000

Daily Compound Interest = 508

The daily compound interest for 2 years is Rs 508

**Question 2: **A sum of Rs 5000 is borrowed and the rate is 8%. What is the monthly compound interest for 2 years?

**Solution:**

Monthly Compound Interest = Principal\[\large (1+\frac{Rate}{12})^{12*Time}\] – Principal

Monthly Compound Interest = 5000\[\large (1+\frac{8}{100*12})^{2*12}\] – 5000

Monthly Compound Interest = 5000 * 1.179 – 5000

Monthly Compound Interest = 864.439

The monthly compound interest for 2 years is Rs 864.439

** Question 3: **A sum of Rs. 50,000 is borrowed and the rate of interest is 10%. What is the compound interest for 5 years?

**Solution:**

\[\large Compound\;Interest=P\left ( 1+\frac{R}{100}\right)^{T} – P\]

Here, P = 50,000 ; R = 10% ; T = 5 years ; A=?

\[\large =50000\left ( 1+\frac{10}{100}\right)^{5} – 50000$$=80525.50 – 50000\]

Compound Interest = 30525.50

The compound interest for 5 years is Rs. 30525.50