On a certain sum of money, the difference between the compound interest for a year payable half-yearly and the simple - Maths - Compound Interest

Question

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

Ram Manohar Thakur · Accepted Answer

Dear Student
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

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.