a sum of ₹1000 is invested at 8% simple interest per year. calculate interest at the end of each year. do these interests form an AP. If so find the interest at the end of 30 years making use of this fact.
Answers
Solution :
A sum of Rs. 1000 is invested at 8 % simple interest p.a
We know that
Simple interest = PTR / 100
Simple interest at the end of 1st year = 1000 × 1 × 8 / 100 = Rs. 80
Simple interest at the end of 2nd year = 1000 × 2 × 8 /100 = Rs. 160
Simple interest at the end of 3rd year = 1000 × 2 × 8 /100 = 240
Similarly, we can calculation for 4th year, 5th year and so on. So the interest at the end of 1st year, 2nd year, 3rd year...... respectively are :
80, 160, 240, .......
Given : These interests for consecutive years form an AP and also their common difference is same
First term of the AP ( a ) = Rs. 80
Common difference ( d ) = a₂ - a₁ = 160 - 80 = 80
We are asked to find the interest at the end of 30 yewars
So interest at the end of 30 years would the 30th term of the AP
Using the nth term of AP formula
Interest at the end of 30 years = 30th term = a₃₀ = a + ( 30 - 1 )d = 80 + 29( 80 ) = 80( 30 ) = 2400
Hence the interest at the end of 30 years is Rs. 2400.
Answer:
Step-by-step explanation:
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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