If the difference between compound interest compounded half yearly and the simple interest on a sum of 10% p.a. for one year is ₹ 25. Then find sum.
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Interest compounded half yearly in this case means 5% interest at intervals of six months, or twice in a year.
Effective interest rate = A + B + AB/100
5 + 5 + 5x5/100 = 10.25%
Simple interest = 10%
Difference is 0.25% and is given as Rs 25.
=> 0.25/100 x s = 25
=> s = 25 x 100/0.25 = Rs 10,000
Check :
SI on 10000 @ 10% = Rs 1000
CI on 10,000 @ 10% compounded half yearly = Rs 1025
Difference = Rs 25
Effective interest rate = A + B + AB/100
5 + 5 + 5x5/100 = 10.25%
Simple interest = 10%
Difference is 0.25% and is given as Rs 25.
=> 0.25/100 x s = 25
=> s = 25 x 100/0.25 = Rs 10,000
Check :
SI on 10000 @ 10% = Rs 1000
CI on 10,000 @ 10% compounded half yearly = Rs 1025
Difference = Rs 25
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