Interest formulas mainly refer to the formulas of simple and compound interests. The simple interest (SI) is a type of interest that is applied to the amount borrowed or invested for the entire duration of the loan, without taking any other factors into account, such as past interest (paid or charged) or any other financial considerations. Simple interest is generally applied to short-term loans, usually one year or less, that are administered by financial companies. The same applies to money invested for a similarly short period of time. The simple interest rate is a ratio and is typically expressed as a percentage.

On the other hand, the compound interest is the interest which is calculated on the principal and the interest that is accumulated over the previous tenure. Thus, the compound interest (CI) is also called as “interest on interest”. It plays an important role in determining the amount of interest on a loan or investment. The formulas for both the compound and simple interest is given below.

## Interest Formulas for SI and CI

The **Interest formulas** are given as,

Formulas for Interests (Simple and Compound) | |
---|---|

SI Formula | S.I. = Principal × Rate × Time |

CI Formula | C.I. = Principal (1 + Rate)^{Time} − Principal |

### Example Problem Using Interest Formulas

**Question 1: A sum of Rs 4000 is borrowed and the rate is 7%. What is the simple and compound interest for 2 years?**

Solution:

Simple Interest = Principle × Rate × Time = PTR/100

⇒ Simple Interest = 4000 × (7 ⁄ 100) × 2

⇒ Simple Interest = 560

∴ The simple Interest for 2 years is Rs. 560

Compound Interest = Principal × (1 + Rate)^{Time} − Principal

So, Compound Interest = 4000 × (1 + 7 ⁄ 100)^{2} − 4000

⇒ Compound Interest = (4000 × 1.1449) − 4000

⇒ Compound Interest = 580

∴ The compound interest for 2 years is Rs. 580

**Question 2: A sum of Rs. 25000 becomes Rs. 30000 at the end of 4 years when calculated at simple interest. Find the rate of interest.**

Solution:

Given,

Principal = P = Rs. 25000

Time = T = 4 years

Amount at the end of 4 years = Rs. 30000

SI = Rs. 30000 – Rs. 25000 = Rs. 5000

SI = PTR / 100

⇒ R = SI × 100 / PT

⇒ R = 5000 × 100 /( 25000 × 4)

⇒ R = 5%

Hence, the rate of interest = 5%

**Question 3: Find the compound interest on Rs. 13000 at 10% for 2 years, compounded annually**.

Solution:

Given,

Principal = P = Rs. 13000

Rate of interest = r = 10%

Time = t = 2 years

Amount on CI = P(1 + r/100)^{2}

= 13000(1 + 10/100)^{2}

= 13000 (1 + 0.1)^{2}

= 13000(1.1)^{2}

= 13000 × 1.21

= 15730

CI = Amount on CI – Principal

= Rs. 15730 – Rs. 13000

= Rs. 2730

Therefore, the compound interest = Rs. 2730