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ICSE Class 9 Answered

On a certain sum of money, the difference between the compound interest for a year, payable half yearly, and the simple interest for a year is Rs. 16. Find the sum lent out if the rate of interest in both the cases is 8%.
Asked by Topperlearning User | 31 Jul, 2017, 02:34: PM
answered-by-expert Expert Answer

Let the sum of the money lent out = Rs. x

begin mathsize 12px style Amount space received space after space one space year equals straight x open parentheses 1 plus straight r over 100 close parentheses to the power of 2 straight n end exponent equals straight x open parentheses 1 plus 8 over 200 close parentheses to the power of 2 cross times 1 end exponent equals straight x open parentheses 1 plus 1 over 25 close parentheses squared equals straight x open parentheses 26 over 25 close parentheses squared equals 676 over 625 Compound space interest space left parenthesis straight C. straight I. right parenthesis equals 676 over 625 straight x minus straight x equals fraction numerator 676 straight x minus 625 straight x over denominator 625 end fraction equals Rs. space 51 over 625 and space simple space interest space left parenthesis straight S. straight I. right parenthesis equals Rs. space fraction numerator straight x cross times 8 cross times 1 over denominator 100 end fraction equals Rs. space fraction numerator 2 straight x over denominator 25 end fraction Difference space between space straight C. straight I. space and space straight S. straight I. space equals space Rs. space 16 rightwards double arrow 51 over 625 straight x minus 2 over 25 straight x equals 16 fraction numerator 51 straight x minus 50 straight x over denominator 625 end fraction equals 16 straight x equals 16 cross times 625 equals 10 comma 000 Hence comma space the space sum space lent space out space is space Rs. space 10 comma 000 end style

                                                                                                                 

Answered by | 31 Jul, 2017, 04:34: PM

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