Question

find CI on 12600 for 2 years at 10 per annum compounded annually

Answer 1

Answer:

Compound Interest = ₹2,646.

Step-by-step explanation:

We've been given Principal, time,rate and interest is compounded annually. We've to calculate Compound Interest. We can calculate Compound Interest by two methods. So let's do :-

Calculating C.I. Using. 1st Method

In this method first we've to calculate amount first then after that we will calculate Compound Interest.

Principal (P) = ₹12,600.

Time (n) = 2years.

Rate (R) = 10% p.a.

C.I. = ?

$\bf \: \: \: \: \: \: {A=P\bigg\lgroup1+\dfrac{R}{100}\bigg\rgroup}^n \\ \\ \\:\implies\bf{A=12600\bigg\lgroup1 + \frac{1 \cancel0}{10\cancel{0}} \bigg \rgroup^{2}} \\ \\ \\:\implies\bf{A=12600\bigg\lgroup1 + \frac{1}{10}\bigg\rgroup}^2 \\ \\ \\:\implies\bf{A=12600\bigg\lgroup \frac{10 + 1}{10} \bigg \rgroup^{2} \: \: \: \: \: \: } \\ \\ \\:\implies\bf{A=12600\bigg\lgroup \frac{11}{10} \bigg \rgroup^{2} \: \: \: \: \: \: \: \: \: \: \: } \\ \\ \\:\implies\bf{A=126 \cancel0 \cancel0 \times \frac{11}{1 \cancel0} \times\frac{11}{1 \cancel0}} \\ \\ \\:\implies\bf{A=126 \times 11 \times 11} \: \: \: \: \: \: \: \: \\ \\ \\:\implies\bf{A=126 \times 121 \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \\ \\ \therefore \: \bf{Amount=₹15,246.}$

Now,

C.I. = A - P

= 15246 - 12600

$\therefore$ Compound Interest = ₹2,646.

Calculating C.I. Using 2nd Method

In this method we've to just put the values in the formula and after calculating it we will get our Compound Interest.

Principal = ₹12,600.

Time = 2years.

Rate = 10%p.a.

$\bf{C.I. = P\bigg\lgroup1 + \dfrac{R}{100}\bigg\rgroup^n-P} \\\\\\: \implies\bf{C.I. = 12600\bigg\lgroup1 + \dfrac{1 \cancel0}{10 \cancel0}\bigg\rgroup^2-12600} \\ \\ \\: \implies\bf{C.I. = 12600\bigg\lgroup1 + \dfrac{1}{10}\bigg\rgroup^2-12600} \\ \\ \\: \implies\bf{C.I. = 12600\bigg\lgroup\dfrac{10 + 1}{10}\bigg\rgroup^2-12600} \\ \\ \\: \implies\bf{C.I. = 12600\bigg\lgroup\dfrac{11}{10}\bigg\rgroup^2-12600 \: \: \: \: \: \: \: } \\ \\ \\: \implies\bf{C.I. = 12600 \times \frac{11^{2} }{1 {0}^{2} } -12600 \: \: \: \: \: \: \: \: \: } \\ \\ \\: \implies\bf{C.I. = 126 \cancel{00} \times \frac{121}{1 \cancel{00}} -12600} \\ \\ \\: \implies\bf{C.I. = 126 \times 121-12600 \: \: \: \: \: \: \: \: \: \: \: } \\ \\ \\: \implies\bf{C.I. = 15246-12600 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \\ \\ \therefore \: \bf{Compound\:Interest=₹2,646\: \: \: \: \: \: \:}$

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Answer 2

$\small\bold\red{given:-}$

• Amount = ₹12600
• Time (n) = 2 year
• Rate = 10%

$\small\bold\green{To \: Find:-}$

• compound interest p.a

$\small\bold\blue{Solution:-}$

$A = P(1 + \frac{R}{100} ) {}^{n}$

$A = 12600(1 + \frac{10}{100} ) {}^{2}$

$A = 12600( \frac{110}{100} ) {}^{2}$

$A = 12600 \times \frac{110}{100} \times \frac{110}{100}$

$A = 126 \times 11 \times 11$

$A = 15246Rs.$

$C.I = A - P$

$C.I = 15246 - 12600 \\ C.I = 2646Rs. \: \: \: \: \: \: \: \:$

Hence ,

• Compound Interest is ₹2646.