the difference between CI and si for 3/2 years at 10% p.a, compounded half yearly is Rs.76.25 find the sum.
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Answers
Aloha !
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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
Note : This method is only for Aptitude Test Takers and not suitable for Homework for school kids.
If the interest componded half yearly, it becomes r/2 =10/2=5%
Now ₹ 25 is the interest on the interest that is gained after later half of the year (i.e 6 months.).
So, we can say 5% = 25, then 100% = 500
₹500 is the interest received after 6 months @ 5% .
as 5% = 500, 100% = 10000{sum}
We can generate a formula for this half yearly compounded i.e
=( 100/r/2)^2 × difference