**Simple Interest **

*Principal:*The money borrowed or lent out for a certain period is called the*principal*or the*sum*.*Interest:*Extra money paid for using other's money is called*interest*.- Simple Interest (S.I.):If the interest on a sum borrowed for certain period is reckoned uniformly

then it is called*simple interest*.Let Principal = P, Rate = R% per annum (p.a.) and Time = T years.

Then Simple Interest= (PxRxT)/100. - So in order to find the Principal We can use formula,

P= (SIx100)/RxT

Here R is in terms of percentage % - Similarly for calculation of time we use formula,

T = (100xSI)/PxR(i). Simple Interest = P x R x T 100 (ii). P = 100 x S.I. ; R = 100 x S.I. and T = 100 x S.I. . R x T P x T P x R

1) Dick takes a loan of Rs. 8,000 to buy a used truck at the rate of 9 % simple Interest.Calculate the annual interest to be paid for the loan amount.

**Solution:**

From the details given in the problem Principle = P = Rs. 8,000 and R = 9% or 0.09 expressed as a decimal.

As the annual Interest is to be calculated, the time period T =1.

Plugging these values in the simple Interest formula,

I = P x T x R

= 8,000 x 1 x 0.09

= 720.00

**Annual Interest to be paid = Rs.720**

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2) Steve invested Rs. 10,000 in a savings bank account that earned 2% simple interest. Find the interest earned if the amount was kept in the bank for 4 years.

**Solution:**

Principle P = Rs 10,000 Time Period T =4 years and Rate of Interest = 2% = 0.02

Plugging these values in the simple Interest formula,

I = PX T X R {here we have take R in terms of fraction so no need of dividing by 100.

= 10,000 X 4 x 0.02

= Rs. 800

**Interest earned for the investment = Rs. 800**

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3) Ryan bought Rs.15,000 from a bank to buy a car at 10% simple Interest. If he paid Rs. 9,000 as interest while clearing the loan, find the time for which the loan was given.

**Solution :**Principle = Rs 15,000 Rate of Interest R = 10% and the Interest paid = I = Rs. 9,000. And T is to be found.

T = (I x 100) /(PR)

= 9000/(15,000 x 0.10)

= 6 years.

**The loan was given for 6 years.**

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**Solved examples on Simple Interest**

4) In how much time will the simple interest on Rs. 3,500 at the rate of 9% p.a be the same as simple interest on Rs. 4,000 at 10.5% p.a for 4 years?

**Solution : In first step we need to find the Simple Interest on Principal Rs 4000/-**

S.I on Rs. 4,000 at rate 10.5% = 10.5/100 = 0.105 for 4 years

S.I = ( P x R x T) /100

= 4000 x 0.105 x 4

S.I = Rs. 1,680

Now as we have found the interest on Rs. 4000 and as per the question we know the interest on Rs 4000 is same as that on Rs 3500 at 9% for unknown time period,

The interest of Rs. 1,680 is the same as that on Rs.3,500 at 9% p.a for suppose 't' years.

Therefore,

1680 = (3500x9xT)/100.

**Time = t = 5.33years.**