State if the following is true or false.

In following situation, the list of numbers involved arithmetic progression.

The amount of money in the account every year when Rs. 10000 is deposited at compound interest 8% per annum.

Question

State if the following is true or false.

In following situation, the list of numbers involved arithmetic progression.

The amount of money in the account every year when Rs. 10000 is deposited at compound interest 8% per annum.

Accepted Answer

Given that,The amount of the money in the account every year when rupees 10000 is deposited at compound interest

8%
   per annum. Now, The value of interest earned in the first year =10000×8%⇒The value of interest earned in the first year=10000×8100⇒The value of interest earned in the first year=800Therefore,  the total amount outstanding after one year will be,⇒a1=800+10000⇒a1=10800Similarly,  The value of interest earned in the second year =10800×8%⇒The value of interest earned in the second year =10800×8100⇒The value of interest earned in the second year =864Therefore, the total amount outstanding after the second year,⇒a2=10800+864⇒a2=11664Again,  The value of interest earned in the third year =11664×8%⇒The value of interest earned in the third year =11664×8100⇒The value of interest earned in the third year=93312100⇒The value of interest earned in the third year =933.12Therefore, the total amount outstanding after the third year will be,⇒a3=933.12+11664⇒a3=12597.12Therefore, the series is 10800,11664,12597.12,.... Now, the common difference will be,⇒a2-a1=11664-10800⇒a2-a1=864And,⇒a3-a2=12597.12-11664⇒a3-a2=933.12Difference between the 3rd and the 2nd term is not equal to the difference between the 2nd and 1st term. Hence, it doesn’t form an AP.The list of numbers don’t form an arithmetic progression.Therefore, the statement is false.Hence, option 2 is correct.