A sum of money at compound interest amounts i | vedclass

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(D) The difference in the amount of money over one year represents the compound interest for that year.Hence,the interest for the third year is Rs. $[

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$6 \%, Rs. 2500$

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(D) The difference in the amount of money over one year represents the compound interest for that year.Hence,the interest for the third year is Rs. $[2977.54 - 2809] = Rs. 168.54$.This interest is earned on the principal amount at the end of the second year,which is Rs. $2809$.Using the formula for simple interest for one year (since $CI$ for one year equals $SI$):$R = \frac{Interest 	imes 100}{Principal 	imes Time} = \frac{168.54 	imes 100}{2809 	imes 1} = \frac{16854}{2809} = 6 \%$.Now,to find the original sum $P$,we use the amount formula for $2$ years:$A = P(1 + \frac{R}{100})^n$$2809 = P(1 + \frac{6}{100})^2$$2809 = P(1.06)^2$$2809 = P(1.1236)$$P = \frac{2809}{1.1236} = 2500$.Thus,the rate of interest is $6 \%$ and the original sum is Rs. $2500$.

$A$ sum of money at compound interest amounts in two years to Rs. $2809,$ and in three years to Rs. $2977.54.$ Find the rate of interest and the original sum.

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