**☛ GETTING STARTED**

**☛ Interest:** An additional amount paid back by a borrower to the lender for using the latter’s money.

**☛** The two common ways of calculating the interest are – **simple interest** and **compound interest**

**SIMPLE INTEREST**

☛ This is a direct application of the Unitary method.

☛ The amount given out on loan is known as **‘Principal’**

☛ Amount paid as interest for every Rs.100 borrowed for a year is known as ‘**rate of interest’ and is expressed as ‘p.c.p.a’ ( Per cent per annum)**

Eg. Ram borrowed Rs.10,000 from Manilal under the condition that Ram has to pay an **interest at 10 per cent per annum**. Ram being naive, did not understand the meaning of it.

Manilal further explains: **For every Rs.100 borrowed for a year , Ram has to pay Rs. 10**.

Ram calculates that **for one year of borrowing**, **he has to pay Rs. 10000*10/100. **

**= Rs. 1000**

SI for 1 year of borrowing is PR/100

Ram says, I will repay the amount **after 2 years**.

Manilal replies, “My terms are fixed. You will incur interest for both the years then”

Ram calculates again. The interest was Rs.1000 for 1 year.

For the **second year also, the interest will be Rs.1000**

So, it should be

** Rs. 1000 x 2**** =Rs.2000 for 2 years**

If it was PR/100 for 1 year, it would be **PNR /100 where N is the number of years and R is rate of interest**

So, generalizing,

** SI for any given sum = PNR/100**

It is to remembered that **the interest incurred every year for the borrowed sum will be the same, which is PR/100**

** COMPOUND INTEREST**

☛ It is the **interest paid on both the borrowed capital as well as the interest accrued for the previous interest** generated on the sum

**Calculate the compound interest for Rs. 2400 @ 8% for 2 years.**** Soln:**

For the 1 st year:

8/100 x 2400

= **Rs. 192** (Since there is no previous interest )

For the 2nd year:

8/100 x (**2400+192)** (Since the interest for 1st year is Rs.192 )

=**Rs. 207.36**

Hence the CI for 2 years is (Rs. 192 + Rs.207.36) = **Rs.399.36**

FORMULA FOR COMPOUND INTEREST

**Note:** CI and SI are equal for the first year. In all other cases, CI is always greater than SI.

**TIP:**

When number of year < 2, it is better to use the concepts as it is less time consuming

**Compounding Half yearly and Quarterly**

For Compounding Half-Yearly,

**R’= R/2**

**N’= 2N**

Similarly, for Compounding Quarterly,

**R’= R/4**

**N’= 4N**

**Finding the CI when N (no. of years) is in mixed fraction**

Step 1 : Find the Accrued amount for the integer number of years

Step 2: Find SI for the remaining fraction number of years using the amount obtained in Step 1 as Principal

Step 3: Add the SI generated in Step 2 to the amount generated in Step 1 and subtract the Principal

**Eg. Find the CI for Rs. 2500 lent out at 10% CI for 7/2 years**

**Soln:**

P= 2500; R = 10% ; N = 7/2

**Step 1:**

Amount Matured in 3 years

= 2500 x (11/10)^{3}

= **Rs.3327.5**

** **

**Step 2:**

Find SI for 1/2 years using Rs.3327.5 as principal.

SI for 1/2 year

= 3327.5 x 0.5 x 10/100

**= Rs. 116.375**

**Step 3:**

Total Amount to be repaid at end of 7/2 years

=Rs.3327.5+116.375

=**Rs. 3443.875**

CI for 7/2 years

= 116.375+3327.5-2500

=3443.875 – 2500

=Rs. 943.875