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Question

The difference in simple interest and compound interest on a certain sum of money at 623 per annum for 3 years is Rs. 46. Determine the sum.


Solution

Let sum (P)  = Rs. 100
Rate (R) =623%=203% p.a
Period (n) = 3 years
S.I. = =PRT100=100×20×3100×3=Rs.20
Compound interest (C.I) = A - P
=P(1+R100)nP
=P[(1+R100)n1]
=Rs.100[(1+203×100)31]
=Rs.100[(1615)31]
=Rs.100[409633751]
=Rs.100[409633753375]
=Rs.100×7213375=Rs.2884135
Difference in C.I. and S.I.
=Rs.288413520
=Rs.28842700135=Rs.184135
If difference is Rs. 184135, then sum = Rs. 100
if difference is Re. 1, then sum =Rs.100×135184
and if difference is Rs. 46, then sum =Rs.100×135×46184=Rs.3375
Sum = Rs. 3375

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