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CBSE Class 8 Answered

Siris borrowed a sum of163840 at 12.5%pa compound interest anually.on the same dayhe lent out the same amount to sahej at the same rate of interest.But compounded half yearly? Find his gain  
Asked by raushanpathak96 | 06 Dec, 2018, 10:35: PM
answered-by-expert Expert Answer
In the given question, period of lending the money is not given.
Hence this question is worked out for 2 year.
If the user knows the exact period then he/she can workout exactly using the same procedure.
 
We know that the formula for amount,  if interest is annualy compounded is given by
 
begin mathsize 12px style A space equals space P open parentheses 1 plus r over 100 close parentheses to the power of n end style, where A is amount, P is principle, r is annual rate of interest and n is number of years.
instead of annualy compounded, if interest is compounded after m months,
then the amount will be calculated using the formula given below
 
begin mathsize 12px style A space equals space P open parentheses 1 plus open parentheses m over 12 close parentheses open parentheses r over 100 close parentheses close parentheses to the power of k end style, where k is number of times interest is compounded in n years
and k is obtained from the relation k = (n/m)×12

Let us workout this question for two years
 
Amount, if interest is compounded annualy, begin mathsize 12px style A space equals space 163840 cross times open parentheses 1 plus fraction numerator 12.5 over denominator 100 end fraction close parentheses squared space equals space 163840 cross times open parentheses fraction numerator 112.5 over denominator 100 end fraction close parentheses cross times open parentheses fraction numerator 112.5 over denominator 100 end fraction close parentheses space equals space R s. space 2 comma 07 comma 360 end style
Amount, if interest is compounded every 6 months, begin mathsize 12px style A space equals space 163840 cross times open square brackets 1 plus open parentheses 6 over 12 close parentheses open parentheses fraction numerator 12.5 over denominator 100 end fraction close parentheses close square brackets to the power of 4 space equals space 163840 cross times open square brackets fraction numerator 212.5 over denominator 200 end fraction close square brackets to the power of 4 space equals space R s. space 2 comma 08 comma 802.50 end style
Hence for 2 years, his gain is Rs. 1442.50
Answered by Thiyagarajan K | 07 Dec, 2018, 11:48: PM

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