Question

$Rs1000$ is invested at $10$ percent simple interest. Check at the end of every year if the total interest amount in A.P. If this is an A.P. then find interest amount after $20$ years.

Answer 1

It is given that,
Principle $\left(P\right)=Rs1000$
Rate $\left(R\right)=10\%$
Simple interest $S.I=\frac{PRT}{100}$$S.I$ for $1$ year $=\frac{1000\times 10\times 1}{100}=100$$S.I$ for $2$ year $=\frac{1000\times 10\times 2}{100}=200$$S.I$ for $3$ year $=\frac{1000\times 10\times 3}{100}=300$
Hence, the total interest amount is in A.P. i.e $100,200,300,..$
Here,
$a=100$
$d=100$
Now,
$a_n=a+(n-1)d$
$a_{20}=a+(20-1)d$
$=100+19\left(100\right)$
$=100+1900$
$2000$
Hence, the interest amount after $20$ years is Rs. $2000$.