Question

find compound interest on a sum of ₹8000 for 2 years 6 months 5% per annum compounded annually​

Answer 1

Step-by-step explanation:

p×r×t

____

100

=8000×1×6

_________

100

=80×6=480

a=p+i=8000+480=8480

2ndyear

8480×1×6

________

100

424×6

_____

5

2544

_____

5 +8000 your answer will come

Answer 2

Given:-

• Principal = Rs.8000
• Time = 2 years 6 months
• Rate = 5% p.a.

To Find:-

• Compound Interest if the interest is compounded annually.

Solution:-

We are given with time as 2 years 6 months

Let us convert it into years,

We know,

12 months = 1 years

Hence,

$\sf{6\:months = \dfrac{6}{12}}$

=> $\sf{6\:months = \dfrac{1}{2}\:years}$

Now,

• Time = $\sf{2\dfrac{1}{2}\:years}$

We know,

✭ $\bf{A = P\bigg(1+\dfrac{r}{100}\bigg)^n}$

Hence,

$\sf{A = 8000 \bigg(1+\dfrac{5}{100}\bigg)^2\bigg(1+\dfrac{5}{200}\bigg)^{2\times\dfrac{1}{2}}}$

= $\sf{8000\bigg(\dfrac{100+5}{100}\bigg)^2\bigg(\dfrac{200+5}{200}\bigg)^1}$

= $\sf{8000\bigg(\dfrac{105}{100}\bigg)^2\bigg(\dfrac{205}{200}\bigg)^1}$

= $\sf{8000\bigg(\dfrac{105}{100}\bigg)\bigg(\dfrac{105}{100}\bigg)\bigg(\dfrac{205}{200}\bigg)}$

= $\sf{A = \dfrac{18081000000}{2000000}}$

=> $\sf{A = 9040.5}$

Therefore, Amount after 2 years 6 months if the interest is compounded annually will be Rs.9040.5.

We know,

CI = Amount - Principal

CI = 9040.5 - 8000

=> CI = 1040.5

Therefore CI will be Rs.1040.5.

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