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**Simple Interest**

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**Simple Interest (SI)**

If the interest on a sum borrowed for certain period is calculated
uniformly, it is called simple interest(SI). (fix percentage of
principal)

**Principal (sum)**

Principal (or the sum) is the money borrowed or lent out for a certain period. It is denoted by P.

**What is Amount?**

The Addition of Simple Interest and Principle is called the Amount.

**A = S.I + P ( Principle )**

**Interest**

Interest is the extra money paid by the borrower to the owner (lender) as a form of compensation for the use of the money borrowed calculated on the basis of Principle.

**Time**

This is the duration for which money is lend / borrowed.

**Rate of Interest**

It is the rate at which the interest is charge on principal.

**What is Per annul means?**

"Rate of interest R% per annum" means that the interest for one year on a sum. If not stated explicitly, rate of interest is assumed to be for one year.

**Formulas Need to Remember**

**S.I =[( P X R X T )/( 100 )].**

Where P = Principle, R = Rate of per annul, T = Number of years

**From the above formula , we can derive the followings**

P=(100×SI)/ RT

R=(100×SI)/ PT

T=(100×SI)/ PR

**Some Tricks to Solve easily**

**Trick 1:**

If a sum of money becomes

**“n”**times in

**“T years”**at simple interest, then the rate of interest per annum can be given be

**Trick 2**:

If an amount

**P1**is lent out at simple interest of

**R1%**per annum and another amount

**P2**at simple interest rate of

**R2%**per annum, then the rate of interest for the whole sum can be given by

**Trick 3:**A sum of money at simple interest

**n1**itself in

**t1 year**. It will become

**n2**times of itself in (If Rate is constant)

**Trick 4:**

In what time will the simple interest be

**“n”**of the principal at

**“r %”**per annum:-

**rt =n x 100**

**Trick 5:**

If a certain sum of money is lent out in n parts in such a manner that equal sum of money is obtained at simple interest on each part where interest rates are

**R1, R2, ... , Rn**respectively and time periods are

**T1, T2, ... , Tn**respectively, then the ratio in which the sum will be divided in n parts can be given by

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

**Solution:**

**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.

**Ex. 2.**Find the simple interest on Rs.306. 25 from March 3

^{rd}to July 27

^{th}at per annum.

Solution:

Interest = Rs.

= = Rs. 4.59

**To find principal:-**

Since I =

**Ex.3.**What sum of money will produce Rs.143 interest in years at p.c. simple interest?

**Solution:**

Let the required sum be Rs. P. Then

Rs P =

**To find rate %:-**

Since I =

**Ex. 4.**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 Rs500. Find the rate of interest per cent annum.

**Solution:**

Here, P =Rs468.75, t = or

I = Rs.(500-468.75) = Rs.31.25

rate p.c. =

**To find Time:-**

Since, I = P t r / 100

**Ex. 5.**In what time will Rs.8500 amount to Rs.15767.50 at per cent per annum?

**Solution:**

Here , interest = Rs.15767.50 – Rs.8500 =Rs.7267.50

**Miscellaneous Examples on Simple Interest:-**

**Ex.6:**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.

**Solution:**

Let principal = P, time = t year, rate = t

Then,

Hence, rate = %

**Direct formula:**

**Rate**= time = %

**Ex. 7:**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.To fetch an interest of 1520 in six years, money did he deposit?

**Solution**

Let his deposit be = Rs 100

Interest for first 2 yrs = Rs 6

Interest for next 3 yrs = Rs 24

Interest for the last year = Rs 10

Total interest = Rs 40

When interest is Rs 40, deposited amount is Rs 100

when interest is Rs 1520, deposited amount = = Rs 3800

**Direct formula:**

**Principle = Interest*100/r**

_{1}t_{1}+r_{2}t_{2}+r_{3}t_{3}…**= =Rs 3800**

**Ex.8:**A sum of money doubles itself in 10 years at simple interest. What is the rate of interest?

**Solution:**

Let the sum be Rs 100

After 10 years it becomes Rs 200

Interest = 200 - 100 = 100

Then, rate = =

**Direct formula:**

**Time × Rate = 100 (Multiple number of principal – 1)**

Or, Rate =

Using the above formula rate =

**Ex.9:**A sum was put at a certain rate for 2 yrs. Had it been put at 3% higher rate, it would have fetched Rs 300 more. Find the sum.

**Solution:**

Let the sum be Rs x and the original rate be y% per annum. Then, new rate = (y+3) % per annum

xy +3x – xy =15,000 or, x =5000

Thus, the sum =Rs 5000

**Gradestack Method :**Direct Formula

Sum = =

**Ex.10.**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.

**Solution:**

Let the sum be Rs.x , then, at 4% rate for 4 yrs the simple interest = = Rs.

At 5% rate for 3 yrs the simple interest = = Rs

Now, we have, or,

Or, x= Rs 8000

**Gradestack Method : For this type of question**

Sum = = Rs 8000

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