Question

a sum of rupees 18000 is invested for 2 years at 5% per annum compound interest a)calculate interest for 1 year b)principal for the second year c) interest for the second year d)final amount at the end of the year e)compound interest earned in two years​

Answer 1

Given:-

• Principal = Rs.18000
• Time = 2 years
• Rate = 5%

Solutions:-

a) Calculate interest for 1st year.

We know,

$\sf{A = P\bigg(1+\dfrac{r}{100}\bigg)^t}$

= $\sf{A = 18000\bigg(1+\dfrac{5}{100}\bigg)^1}$

= $\sf{A = 18000\bigg(1+\dfrac{1}{20}\bigg)^1}$

= $\sf{A = 18000\bigg(\dfrac{20+1}{20}\bigg)^1}$

= $\sf{A = 18000\bigg(\dfrac{21}{20}\bigg)}$

= $\sf{A = 18900}$

$\sf{CI = A - P}$

= $\sf{CI = 18900-18000}$

= $\sf{CI = Rs.900}$

Therefore Interest after 1 year will be Rs.900.

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b) Principal for the 2nd year.

Amount for the 1st year is the principal for the 2nd year.

Therefore principal for the 2nd year = Rs.18900.

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c) Interest for the second year.

$\sf{A = P\bigg(1+\dfrac{r}{100}\bigg)^t}$

= $\sf{A = 18900\bigg(1+\dfrac{5}{100}\bigg)^1}$

= $\sf{A = 18900\bigg(\dfrac{100+5}{100}\bigg)^1}$

= $\sf{A = 18900\bigg(\dfrac{105}{100}\bigg)^1}$

= $\sf{A = 189\times105}$

= $\sf{A = 19845}$

$\sf{CI = A-P}$

= $\sf{CI = 19845 - 18000}$

= $\sf{CI = 1845}$

Therefore CI for the second year will be Rs.1845

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d) Final amount after end of 2 year.

$\sf{A = P\bigg(1+\dfrac{r}{100}\bigg)^2}$

= $\sf{A = 18000\bigg(1+\dfrac{5}{100}\bigg)^2}$

= $\sf{A = 18000\bigg(\dfrac{105}{100}\bigg)^2}$

= $\sf{A = 18000\times\dfrac{105}{100}\times\dfrac{105}{100}}$

= $\sf{A = 19845}$

Therefore final amount at the end of two year will be Rs.19845.

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e) CI earned in two years.

CI earned in two years will be Rs.1845 refer to solution (c)

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Formulas used:-

$\sf{A = P\bigg(1+\dfrac{r}{100}\bigg)^t}$

CI = A-P

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