Rupees 820 is nvested at the rate of 8 percent simple nterest in abank .

a) find the interest after 1 year,2year,3year

b)is the sequence of interest an arithmatic sequence ?

c) compute the interest after 23 year .

Answer :

Principle amount  P =  820
Rate of interest r  = 8%
And
We know Simple interest  = $\frac{P \times r \times t }{100}$
So,
a ) Interest after 1 year = $\frac{820 \times 8 \times 1}{100} = \frac{6560}{100}$ =  65.60
And
Interest after 2 year = $\frac{820 \times 8 \times 2}{100} = \frac{13120}{100}$ =  131.20
And
And
Interest after 3 year = $\frac{820 \times 8 \times 3}{100} = \frac{19680}{100}$ =  196.80

b  ) Now we check that these interest are in A.P. or not , as we know common difference of A.P. always equal , so

131.20 - 65.60 =  196.80 - 131.20

65.60 = 65.60                   ( Satisfied )

So, we can say that sequence of interest are in arithmetic sequence .

C ) we know Common difference d  =  65.60
And
first term =  65.60  (  interest after 1 year )
And
Number of terms n = 23
And
we know formula for n^th term in A.P. , As:
T_n = a + ( n  -  1 ) d , So

T₂₃ =  65.60 + ( 23 - 1 ) 65.60

T₂₃ =  65.60 +22$\times$ 65.60

T₂₃ =  65.60 + 1443.2

T₂₃ = 1508.80
So,
Interest after 23 year  =  Rs 1508.80                                                      ( Ans )