Divya deposited Rs. 1000 at compound interest | vedclass

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(B) The formula for the amount $A$ under compound interest is $A = P(1 + r/100)^n$,where $P = 1000$,$r = 10$,and $n$ is the number of years.Amount at

Vedclass · Accepted Answer

No,it does not form an $AP$.

Vedclass · Answer

(B) The formula for the amount $A$ under compound interest is $A = P(1 + r/100)^n$,where $P = 1000$,$r = 10$,and $n$ is the number of years.Amount at the end of the $1^{st}$ year: $A_1 = 1000(1 + 10/100)^1 = 1000(1.1) = 1100$.Amount at the end of the $2^{nd}$ year: $A_2 = 1000(1 + 10/100)^2 = 1000(1.21) = 1210$.Amount at the end of the $3^{rd}$ year: $A_3 = 1000(1 + 10/100)^3 = 1000(1.331) = 1331$.The sequence of amounts is $1100, 1210, 1331, \ldots$.To check if it is an $AP$,we calculate the common difference:$A_2 - A_1 = 1210 - 1100 = 110$.$A_3 - A_2 = 1331 - 1210 = 121$.Since $A_2 - A_1 
eq A_3 - A_2$,the difference between consecutive terms is not constant.Therefore,the sequence does not form an $AP$.

Divya deposited $Rs. 1000$ at compound interest at the rate of $10\%$ per annum. The amounts at the end of the first year,second year,third year,$\ldots,$ form an $AP$. Justify your answer.

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