**Interest:**It is the extra money paid by the borrower to the owner (lender) as a form of compensation for the use of the money borrowed.

**Simple Interest (SI):**

SI = PRT/100

P=(100*SI)/RT

R=(100*SI)/PT

T=(100*SI)/PR

Where,

P= Principle or sum (It is the money borrowed or lent out for a time period T)

R=Rate at which interest is charged on P per annum (Thus, 6 p.c. means that Rs.6 is the interest on Rs.100 in one year.

T=time period

A = Amount (The Addition of Interest and Principle i.e. A = (I + P)

**Note:
Simple interest is only based on the principal amount of a loan, while compound interest is based on the principal amount and the accumulated interest.**

**Example 1. **Find the simple interest on Rs.400 for 5 years at 6 per cent.

Solution:

SI = 400*6*5/100=120

**Interest for a number of days**

When the time is given in days or in years and days, 365 days are reckoned to a year.

But when the time is given in months and days, 12 months are reckoned to a year

and 30 days to the month.

The day on which the money is paid back should be include be but not the day on which it is borrowed, ie, in counting, the first day is omitted.

**Example 2. **Find the simple interest on Rs.306.25 from March 3^{rd} to July 27^{th} at 15/4% per annum.

**Solution:**

Interest = (306.25*(15/4)*146)/365.

Days = (28+30+31+30+27) {As 3rd March to be omitted and 27^{th} July to be considered. }

= 4.59

**Example 3. **A sum of Rs.468.75 was lent out at simple interest and at the end of 1 year 8 months the total amount was Rs 500. Find the rate of interest per annum.

**Solution:**

SI=A-P

=> 500-468.75= 31.25

R=SI. 100/(P*T)

= (31.25*100)/(468.75*5/3)

= 781.25

**Practice Questions:**

- In what time will Rs.8500 amount to Rs.15767.50 at 9/2 per cent per annum?
- The simple interest on a sum of money is 1/9
^{th}of the principal, and the number of years is equal to the rate per cent per annum. Find the rate per cent. - The rate of interest for the first 2 yrs is 3% per annum, for the next 3 years is 8% per annum and for the period beyond 5 years 10% per annum and earns an interest of RS. 1520. What money did he deposit?
- A sum of money doubles itself in 10 years at simple interest. What is the rate of interest?
- A certain amount was lent at a rate R for 2 yrs. If it been put at 3% higher rate, it would have fetched Rs 300 more. Find the amount?
- The simple interest on a certain sum of money at 4% per annum for 4 yrs is Rs 80 more than the interest on the same sum for 3 yrs at 5% per annum. Find the sum.

** SOLUTIONS**

- SI = 15767.50 – 8500 = 7267.50

T= SI*100/(P*R)

= 7267.50*100/(8500*9/2)

= 19 years - T = R years, SI= P/9

R=(SI*100)/(P*T)

= ((P/9)*100)/(P*R)

R^{2}= 100/9

R=10/3 -
Let money deposited = P

1520 = [(P*3*2)/100] + [P*8*3/100] + [P*10*1/100] 1520 = P*40/100

P= 1520*100/40

P= 3800 -
SI = P {As amount (SI + P) = 2P)

P = P*R*10/100

R= 10% -
Say at rate R Interest = SI, and the amount = P

SI = P*R*2/100 …………………..(1)

Now, R = R+3 and SI = SI+300

SI+300 = P*(R+3)*2/100 ………..(2)

From eq. (1) and (2)

(P*R*2/100) + 300 = P*(R+3)*2/100

30000 = 6*P

P=5000 - 80 = [P*4*4/100] – [P*3*5/100] P=8000

**Shortcut: P = Difference in SI*100/(R1*T1 + R2*T2)**