Question

A sum of money is lent out at compound interest for two years at 20% p.a.,C.I. being reckoned yearly. If the same sum of money is lent out at compound interest at the same rate percent per annum,C.I. being reckoned half yearly, it would have fetched 482rs more by way of interest. Calculate the sum of money lent out.

Answer 1

Answer:

For first case r = 20% p.a.

 n = 2 years





Difference between two interest 

= ₹ 46.41 - ₹ 44.00 = ₹ 2.41

 If differences  is ₹ 2.41 then principal be ₹ 100

 If differences  is ₹ 482 then principal will be 

= ₹ 100/2.41 x 482

= ₹ 100 x 482/241 x 100

= ₹ 100 x 100 x 2

= ₹ 20000

∴ Sum is ₹ 20000.

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Answer 2

Answer:

₹20, 000

Step-by-step explanation:

Let the sum of money lent out be Rs. x

In the Ist case:

A 1

=Rs x(1+ 100/20)^2 =Rs 36x/25

∴A=P(1+r/100)^n

In the 2nd case:

A 2

=Rs x(1+ 2×100/20)^2×2 =Rs. 10000/14641x

∵A=P(1+2×100/r) ^n×2

According to the question-

⇒ 10000/14641x − 25/36x =482

⇒10000/14641x−14400x =482

⇒241x=4820000⇒x=20000

∴ The sum of money lent out =Rs.20,000

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