the difference between the compound interest and the simple interest on a certain sum of money at 15% per annum for three years is rupees 285.50 then find their sum.
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Solution :
Let principal = Rs p
Rate of interest ( r ) = 15%
Time ( t ) = 3 years
Number of times
Interest paid ( n ) = 3
i ) Simple interest( s.i )=(ptr)/100
s.i = ( p × 3 × 15 )/100
= 0.45p ----( 1 )
ii ) compound interest (c.i)
= p[ (1+r/100)ⁿ - 1 ]
= p[ (1+15/100)³ - 1 ]
= p[ (1.15)³ - 1 ]
= p[1.520875 - 1 ]
= (0.520875)p ----( 2 )
iii ) It is given that ,
c.i - s.i= 285.50
=> (0.520875)p - 0.45p = 285.50
=> (0.070875)p = 285.50
=> p = 285.50/(0.070875)
=>p ≈ 402.82
Therefore ,
Principal ( p ) = Rs 402.82
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