# 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 (without using the formula) if the rate of interest in both the cases is 10% per annum.

P=?

R=10%

CI-SI=Rs 180

SI= PRT/100

=10×1P/100=P/10 ___________(i)

CI= P(1+R/200)² -P (HALF YEARLY)

CI= P(210/200)²-P

CI=(441P/400) -P

CI=41P/400___________(ii)

Diff. = CI-SI= 41P/400 - P/10=P/400

But, given, diff.= 180

Therefore,

180=P/400

P=Rs 72000

Regards

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