To fulfill our requirements of certain amount we have to borrow some money from friends or any other organisation. This lent amount is known as principal (P).

We use this money for a certain period which is known as time (T). At a time of returning this money we give some extra money against the use of this money.

This extra money is known as interest which is calculated at a certain rate. This rate is called rate of interest (R) while total money which is returned is called amount (A).

**The interest are of two types**

**Simple Interest**

When interest is calculated only on borrowed money for definite period, then such interest is called simple interest and is denoted by SI.

**Ex: What will be the simple interest on ₹ 200 for 5 yr at 6% per annum.**

(a) ₹70

(b) ₹80

(c) ₹12

(d) ₹50

**Compound Interest**

If after a certain period of time, interest is calculated on interest as well as on principal, then such interest is called compound interest and is denoted by CI.

**Ex: At what rate per cent per annum will ₹2304 amount to 2500 in 2yr at compound interest?**

## Important Formulae

### Formula 1

**Ex: A sum becomes two times in 5 yr at a certain rate of interest. Find the time in which the same amount will be 8 times at the same rate of interest.**

**(a) 35 yr**

**(b) 45 yr**

**(c) 55 yr**

**(d) 25 yr**

### Formula 2

**When interest is calculated per half-year in a compound interest, then rate of interest must be divided by 2 and time must be multiplied by 2.**

** Similarly,**

** when interest is calculated per quarter in compound interest, then rate of****interest must be divided by 4 and time must be multiplied****by 4 for calculation of interest.**

### Formula 3

**Ex: What sum of money at compound interest will amount to ₹4499.04 in 3yr if the rate of interest is 3% for 1st year, 4% for the 2nd year and 5% for the 3rd year?**

(a)6000

(b)4000

(c)5000

(d)6500

### Formula 4

**Ex: Find the compound interest on ₹2000 at 15% p.a. for 2 yr 4 months, compounded annually.**

(a)676.67

(b)576.67

(c)777.25

(d)176.62

### Formula 5

**Ex: The difference between simple and compound interest calculated on same amount at 10% per year for 3 yr, is 15.50 The amount was**

(a)5000

(b)550

(c)500

(d)1500

### Formula 6

**Ex: If a certain sum at compound interest becomes double in 5yr then in how many years, it will be 8 times at the same rate of interest?**

(a) 30 yr

(b) 10 yr

(c) 20 yr

(d) 15 yr