Question

Divya deposited Rs 1000 at compound interest at the rate of 10% per annum. The amounts at the end of first year, second year, third year, ..., form an AP. Justify your answer

Answer 1

Hi,

1) principal = P = Rs 1000

Rate of interest = r = 10%

Time period ( t ) = 1 yr

Amount ( A1 ) = P ( 1 + r / 100 )^t

= 1000 ( 1 + 10 /100 )

= 1000 × 110 / 100

A1 = Rs 1100

2 ) second year principal = A1 = Rs 1100

r = 10 %

Time period ( t ) = 1 yr
Amount at the end of

Second year( A2) = 1100 ( 1 + 10 / 100 )

= 1100 × 110 /100

A2 = Rs 1210

3 ) third year principal = A2 = Rs 1210

r = 10 %

Time period ( t ) = 1 year

A3 = 1210 ( 1 + 10 /100 )

= 1210 × 110 / 100

A3 =Rs 1331

Therefore,

First year , second year ,third year ending Amounts are

1100 , 1210 , 1331 ,...

a2 - a1 = 1210 - 1100 = 110

a3 - a2 = 1331 - 1210 = 121

Therefore ,

a2 - a1 is not equal to ( a3 - a2 )

This is not an A.P

I hope this helps you.

:)

Answer 2

principal = P = Rs 1000

Rate of interest = r = 10%

Time period ( t ) = 1 yr

Amount ( A1 ) = P ( 1 + r / 100 )^t

= 1000 ( 1 + 10 /100 )

= 1000 × 110 / 100

A1 = Rs 1100

2 ) second year principal = A1 = Rs 1100

r = 10 %

Time period ( t ) = 1 yr

Amount at the end of

Second year( A2) = 1100 ( 1 + 10 / 100 )

= 1100 × 110 /100

A2 = Rs 1210

3 ) third year principal = A2 = Rs 1210

r = 10 %

Time period ( t ) = 1 year

A3 = 1210 ( 1 + 10 /100 )

= 1210 × 110 / 100

A3 =Rs 1331

Therefore,

First year , second year ,third year ending Amounts are

1100 , 1210 , 1331 ,...

a2 - a1 = 1210 - 1100 = 110

a3 - a2 = 1331 - 1210 = 121

Therefore ,

a2 - a1 is not equal to ( a3 - a2 )

This is not an A.P

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