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**Simple Interest:**

**Formula**:

1) SI = P x R x T/100

2) Principal = Simple Interest ×100/ R × T

3) Rate of Interest = Simple Interest ×100 / P × T

4) Time = Simple Interest ×100 / P × R

5) If rate of Simple interest differs from year to year, then

Simple Interest = Principal × (R1+R2+ R3…..)/100

The four variables in the above formula are:

SI=Simple Interest

P=Principal Amount (This the amount invested)

T=Number of years

R=Rate of interest (per year) in percentage

**1).** A sum of money is divided into n parts in such a way that the interest on the first part at r_{1}% for t_{1} years, on second part at r_{2}% for t_{2} years, on third part at r_{3}% for t_{3}years and so on, are equal. Then the ratio in which the sum is divided in n part is:

1/r_{1}×t_{1}: 1/r_{2} ×t_{2}: 1/r_{3}×t_{3}

**Example:**

A sum of Rs 7700 is lent out in two parts in such a way that the interest on one part at 20% for 5 yr is equal to that on another part at 9% for 6 yr. Find the two sums.

**Solution:**

Here, R1 = 20% R2 = 9%

T1 = 5 yr T2 = 6 yr

By using formula, ratio of two sums = 1/100 : 1/54 = 27 : 50

Therefore, first part = [27/(27+50)]*7700 = Rs 2700

Second part = [50/(27+50)]*7700 = Rs 5000

**2).** Amount = Principal + S.I = p + [(p x r x t)/100]

**Example:**

What Principal will amount to Rs. 16000 in 6 years at 10% simple interest?

**Solution:**

Let the principal be Rs. p, given rate of interest is 10% and time = 6 years.

Amount received at the end of 6 years = 16000 Rs.

=> 16000 = p + (p x 10 x 6)/100 = p + 6p/10 = 16p/10 => P = 16000 x (10/16) = 1000 x 10 = 10000 Rs.

Principal should be Rs. 10000

**3). **If sum becomes n times in T yr at simple interest, then formula for calculating rate of interest

**R =100(n-1) /T %**

**4).** A sum of money becomes 4 times in 20 yr at SI. Find the rate of interest?

R =100(4-1)/20

=100*3 / 20 =5*3 =15

**5).** If A sum becomes n times in at certain rate of interest .then the time taken in which the same amount will be n times at the same rate of interest:

**= (n-1)/2 × T (n = number of times)**

**6).** If A sum becomes 3 times in at certain rate of interest in 5years .find the time taken in the same amount will be 8 times at the same rate of interest:

=(8-1)/2*5

= 7/2 * 5

=17.5years

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