Question

Question 1 (iv)
In which of the following situations does the list of numbers involved make an arithmetic progression and why?
(iv) The amount of money in the account every year, when Rs. 10000 is deposited at compound interest at $8\%$ per annum.

Answer 1

We know that if Rs. P is deposited at $r\%$ compound interest per annum for n years, the amount at the end of n years will be,
$A=P{(1+\frac{r}{100})}^n$
Therefore, after every year, our money will be
$1000(1+\frac{8}{100}),1000{(1+\frac{8}{100})}^2,1000{(1+\frac{8}{100})}^3\dots \dots$
Clearly, adjacent terms of this series do not have the same difference between them. Therefore, this is not an A.P.