Question

A sum of Rs.1000 is invested at 8% simple interest per annum. Calculate the interest at the end of 1, 2, 3, ……. Years. If the sequences of interests an AP? Find the interest at the end of 30 years.

Answer 1

Simple Interest = P × R × T ÷ 100

So S.I in first yr. ⇒ P x R x T / 100
⇒ 1000 x 1 x 8  ÷ 100 
⇒ 80

In second Yr. ⇒ 1000 x 2 x 8 ÷ 100
⇒ 160
Similarly in third Yr. ⇒ 240

So , we get the A.P. like this i.e. 80, 160, 240

Therefor  a= 80 , d= 80.

we have to find out the interest at the end of 30 yr.
⇒ a$a_{n}$ = a + ( n-1 ) d

⇒ 80 + ( 30 - 1 ) 80
⇒ 80 + 29 × 80
 ⇒ 2400

There fore , the Interest at the end of 30 yrs is 2400

Answer 2

given,
    principal=1000
     rate of interest=8%
       number of years=1 year
      SI=Pnr/100=1000x1x8/100=rs.80
when n=2 years,SI=1000x2x8/100=rs.160
when n=3years,SI=1000x3x8/100=rs.240
the sequence is 
     80,160,240,..........
this is in AP as a,first term=80,d,common difference=80
interest at the end of 30 years,t30=a+(n-1)d
                                                 =80+(30-1)80
                                                 =80+29(80)
                                                 =80+2320
                                                 =2400
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