on certain sum of money the difference between the compound interest for a year payable half-yearly and the simple intrest for a year is Rs 180.Find the sum lent out if the rate of intrest in both the cases is 10% per annum.
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On a certain sum of money, the difference between the compound interest for a year, payable half-yearly, and the simple interest for a year is Rs. 180/−. Find the sum lent out, if the rate of interest in both the cases is 10% per annum.
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Sanha Nausheen
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For ,
N=1year
R=10 %
We have S.I.=
100
PNR
=
100
P×1×10
=Rs0.1P
When interest being compounded for half yearly, for 1 year
We have, N=2
And R=
2
10
=5 %
AndAmount=P(1+
100
R
)
N
=P×(1+
100
5
)
2
=P×1.05
2
=1.1025P
And C.I.=A−P=1.1025P−P=0.1025P
Given, C.I.−S.I.=Rs180
⇒0.1025P−0.1P=Rs180
⇒0.0025P−Rs180
⇒P=Rs72,000
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