Question

Rs 1000 is invested at 10 percent simple interest. Check at the end of every year if the total interest amount is in A.P. If this is an A.P. then find interest amount after 20 years. For this complete the following activity.

Answer 1

It is given that,
Principal (P) = Rs 1000
Rate (R) = 10%
Simple interest (S.I.) =\[\frac{P \times R \times T}{100}\]

Simple interest after an year = \[\frac{1000 \times 10 \times 1}{100} = Rs 100\]

Simple interest after 2 years = \[\frac{1000 \times 10 \times 2}{100} = Rs 200\]

Simple interest after 3 years = \[\frac{1000 \times 10 \times 3}{100} = Rs 300\]

Hence, the total interest amount is in A.P. i.e. 100, 200, 300,....

Here,
a = 100
d = 100
Now,

\[a_n = a + \left( n - 1 \right)d\]

\[ a_{20} = a + \left( 20 - 1 \right)d\]

\[ = 100 + 19\left( 100 \right)\]

\[ = 100 + 1900\]

\[ = 2000\]

Hence, the interest amount after 20 years is Rs 2000.