a sum of money is lent out at compound interest for 2 years at 20% per annum compound interest being reckoned yearly. if the same sum of money is lent out at compound interest at same rate percent per annum compound interest being reckoned half yearly it would have fetched rupees 482 more by way of interest . calculate the sum of money lent out.
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Answer:
Let the sum of money lent out be Rs. x
In the Ist case:
A
1
=Rsx(1+
100
20
)
2
=Rs
25
36x
∴A=P(1+
100
r
)
n
In the 2nd case:
A
2
=Rsx(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