Question

If simple interest of a certain sum of money for 1 year is Rs 50 and compound interest for 2 years is Rs 102, let us calculating the sum of money and the rate of interest.​

Answer 1

Solution :

Let the sum of money be X rupees.

SI on it for a year at a certain rate is rs.50

> xr/100 = 50

> xr = 5000

Now , the CI on X for 2 years is 102

> x [ (1 + r/100)² - 1 ] = 102.

Dividing the first equation by the second equation :

> r/[ ( 1 + r/100)^2 - 1] = 5000/102

> 102r = 5000[ ( 100 + r)² - 10000 ]/10000

> 204r = ( 100 + r )² - 10000

> 10000 + r² + 200r - 10000 = 204r

> r² + 200r = 204r

> r² = 4r

As r ≠ 0, r = 4% per annum .

x = 5000/r

> 1250.

Answer :

The sum of money is Rs. 1250 .

The rate of interest is 4%.

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Answer 2

Given :-

Simple interest of a certain sum of money for 1 year is Rs 50 and compound interest for 2 years is Rs 102,

To Find :-

Principal

Rate

Solution :-

Let the sum of money be x and rate be r

Now

At first the SI is 50

So

⟹ xr/100 = 50

⟹ xr = 100 * 50

⟹ xr = 5000

Now

CI = 102 for 2 years

⟹ x [ (1 + r/100)² - 1 ] = 102.

• xr = 5000

⟹ r/ [( 1 + r/100)² - 1] = 5000/102

On cross multiplication

⟹102r = 5000[ ( 100 + r)² - 10000 ]/10000

⟹102r(2) = (100 + r²) - 10000

⟹ 204r = ( 100 + r )² - 10000

⟹ 10000 + r² + 200r - 10000 = 204r

⟹ [10000 - 10000] + r²  + 200r = 204r

⟹ r² + 200r = 204r

⟹ r² = 204r - 200r

⟹ r² = 4r

⟹ r = 4

Now

⟹ x = 5000/4

⟹x = 1250