SIMPLE INTEREST

Topics

Simple Interest

Important facts

Important formula

Example 1

Example 2

Example 3

Assessment

When money is borrowed, interest is charged for the use of that money for a certain period of time.

The amount to interest depends on the interest rate, the amount of money borrowed and the period of time that the money is borrowed.

Simple Interest

IMPORTANT FACTS

Principal

Interest.

Amount

The money you borrow is known as sum borrowed or principal.

The some extra money paid be the borrower is called as interest paid on principal.

The sum of the principal and the interest paid by the borrower is called as Amount.

IMPORTANT FORMULA

P = Principal I = Interest.

A = Amountr = Rate of interest (in %)

T = Duration of time

A = P + I

I = P × r × T

Example 1

Solution

A sum of money at simple interest becomes amount equal to Rs. 1088 in 3 years and to Rs. 1184 in 4 years. Find the principal and rate of interest.

S.I. for 1 year = Rs (1184 – 1088) = Rs 96

S.I. for 3 year = Rs 96 × 3 = Rs 288Amount = Principal + Interest Principal = Amount – Interest = Rs (1088 – 288) = Rs 800

Let the rate of interest be r% per annum then I = P × r × T 96 = 800 × r × 1∴ r = 96100 %

800 = 12%Hence, Principal = Rs 800 Rate of Interest = 12%

Example 2

Solution

A person lends some amount at interest rate 4.5% per annum of simple interest for certain time. He pays total sum Rs 531 including Rs 81 as interest. Find the time period for which he lend the amount.

IT

P r

...( )I

T iP r

Also, A = P + I

I = P × r × T

⟹ P = A – I …(ii)

On substituting value of (ii) in (i), we get( )

IT

A I r

Given:

A = Rs 531 I = Rs 81 r = 4.5% = 0.045

81

(531 81) 0.045T

⟹ T = 4 years

Example 3

Solution

Rakesh took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If he paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?

Given: P = Rs 1200

Let T = x years and r = x %

I = P × r × T

432 = 1200 × x/100 × x

432 = 12x2

x2 = 36 x = 6

Hence, Rate of Interest = 6%

In how many years will Rs 600 double itself at 10% simple interest? 

Assessment

Find the simple interest at the rate of 5% p.a. for 3 years on that principal which in 4 years and 8 months at the rate of 5% p.a. gives Rs 1200 as simple interest.

At what rate per cent per annum will Rs 4000 yield an interest of Rs 410 in 2 years? 

Karan borrowed Rs 2000 from Sameer at 8% per annum. After 6 year he cleared the amount by giving Rs 2600 cash and a watch to Sameer. Find the cost of the watch.

18

3Years

Answers

Simple Interest = Rs 771.42

15 %

8

Cost of Watch = Rs 560