We are all well versed with the concept of interest. It is the additional amount on the principal amount. It can be expressed in absolute terms but is generally expressed as a percentage on the principal amount. However, do you know there are two major types of interests, namely – simple interest and compound interest? In this article, we will mainly be focusing on compound interest, its meaning, examples, and the compound interest formula.

## Compound Interest Formula

### What is Compound Interest?

Let us first understand the meaning and concept of compound interest and then move onto the compound interest formula. Now interest is the amount we calculate on the principal amount. But in compound interest, we calculate the interest on the principal amount and the interest that has accumulated during the previous period.

Essentially, compound interest is the interest on the interest! So in this method, rather than paying out the interest, it is reinvested and becomes a part of the principal.

As you will have noticed in simple interest, the interest amount remains the same for every period. This is not the case in compound interest. Since the previous interest amount is reinvested, the interest amount increases marginally every year. This is why we have a whole separate compound interest formula to help us calculate the compound interest of any given year.

### Compound Interest Formula

C. I. = P ( 1 + R/100) ^{t }– P

FV = P ( 1 + R/100) ^{t}

Where,

P | Principal Amount |

CI | Compound Interest |

R | Rate of Interest |

t | Time in Years |

FV | Future Value |

### Compound Interest Formula Derivation

To better our understanding of the concept, let us take a look at the derivation of this compound interest formula. Here we will take our principal to be Re.1/- and work our way towards the interest amounts of each year gradually.

Year 1

- The interest on Re 1/- for 1 year = r/100 = i (assumed)
- Interest after Year 1 = Pi
- FV after Year 1 = P + Pi = P(1+i)

Year 2

- Interest for Year 2 = P(1+i) × i
- FV after year 2 = P(1+i) + P(1+i) × i = P(1+i)²

Year ‘t’

- FV after year “t” = P(1+i)t
^{ } - Now substituting actual values we get FV = P ( 1 + R/100)
^{t} - CI = FV – P = P ( 1 + R/100)
^{t }– P

### Solved Examples

Now that we have some clarity about the concept and meaning of compound interest and compound interest formula, let us try some examples to deepen our understanding of the subject.

Q: Mr A decided to open a bank account and opted for the Compound Interest Option at 10%. He invested 10,000 for 3 years. At the end of three years, how much money will he get, and what will be the interest amount. The interest is calculated annually.

Ans: As we already have a formula for future value amount, let us substitute the values

FV = P ( 1 + R/100) ^{t}

FV = 10000 ( 1 + 10/100) ^{5 }

FV = 10000 ( 1.1) ^{5 }

FV = 16,105

CI = FV – P = 6,105/-

Q: Mr B lent money to his son at 8% CI calculated semi-annually. If he lent 1000/- for 2 years, how much will he get back at the end of the 2 years.

Ans: Since the CI is calculated semi=annually

- t= 2t = 4
- r = r/2 = 4

FV = P ( 1 + R/100) ^{t}

FV = 1000 ( 1 + 4/100) ^{4}

FV = 1000 (1.17)

FV = 1170/-