₹ 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.

Simple interest

Simple interest after 1 year

Simple interest after 2 year

Simple interest after 3 year

According to this the simple interest for 4, 5, 6 years will be 400, respectively.

From this and

Amount of simple interest after 20 years

t_n + a + (n – 1) d

Amount of simple interest after 20 years is =

Given: Principal Amount P = 1000

Rate of interest R = 10%

Also,

Simple interest after 1 year

Simple interest after 2 year

Simple interest after 3 year

According to this the simple interest for 4, 5, 6 years will be 400,

500, 600 respectively.

Let first term a = 100

Second term t₁ = 200

Third term t₃ = 300

Common difference d = t₃ – t₂ = 300 – 200 = 100

Amount of simple interest after 20 years

We use n^th term of an A.P. formula

t_n = a + (n – 1)d

where n = no. of terms

a = first term

d = common difference

t_n = n^th terms

⇒ t₂₀ = 100 + (20 – 1) × 100

⇒ t₂₀ = 100 + 19 × 100

⇒ t₂₀ = 100 + 1900 = 2000