Question

A sum of Rs 1000 is invested at 8% simple interest per year . Calculate the interest at the end of each year .Do these interests from an AP? If so ,find the interest at the end of 30 years making use of this fact.

Answer 1

interest in end of first year

= 8/100×1000

=80

interest in end of two year

=2×80

=160

•

•

•interest at end of 30 year

=80×30

=2400

80,160,240,......,2400.

Answer 2

Solution:

$\bf {Simple \: interest = \dfrac {P \times R \times T }{100} }$

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❇So, simple interest at the end of 1st year =

$Rs. \frac {1000 \times 8 \times 1}{100} = Rs.80$

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❇The interest at the end of 2nd year =

$Rs. \frac {1000 \times 8 \times 2 }{100} = Rs. 160$

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❇The interest at the end of the 3 rd year =

$Rs. \frac{1000 \times 8 \times 3 }{100}= Rs. 240$

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▫Similarly, we can obtain the interest at the end of 4th year, 5 th year and so on.

So, the interest at the end of 1st, 2nd, 3rd,... years, respectively are:

80,160,240,....

________________

It is an A.P as the difference between the consecutive terms in list is 80,i.e., d= 80 .also,a = 80 .

So, to find the interest at the end of 30 years, we shall find a_30.

$a_{30} = a + ( 30- 1) d$

$: \implies$d = 80 + 29 × 80 = 2400

So, interest at the end of 30 years will be Rs. 2400.

$\rule{200}4$