Question

2 Find the compound interest on 10,000, at 10% per annum for 3 years.
​

Answer 1

Given that :-

• Principal = ₹ 10,000
• Interest rate = 10% per annum
• Time = 3 years

Need to find :-

• Compound Interest ?

Solution :-

• We know that,

$\leadsto\small{\underline{\boxed{\bf{Amount={P{\bigg(1 + \dfrac{R}{100}{\bigg)}^{T}}}}}}}$

Now, Substitute the given values in the formula : we get,

${\leadsto\displaystyle{ \sf Amount = \: 10000\:\left(\:\: { 1 + \frac{ 1 \cancel0}{10 \cancel0} } \:\right) ^{3} }}$

${\leadsto\displaystyle{ \sf Amount = \: 10000\:\left(\:\: { 1 + \frac{ 1 }{10 } } \:\right) ^{3} }}$

${\leadsto\displaystyle{ \sf Amount = \: 10000\:\left(\:\: { \frac{10 + 1}{10} } \:\right) ^{3} }}$

${\leadsto\displaystyle{ \sf Amount = \: 10000\:\left(\:\: { \frac{11}{10} } \:\right) ^{3} }}$

${\leadsto\displaystyle{ \sf Amount = \: 10000 \times \frac{11}{10} \times \frac{11}{10} \times \frac{11}{10} }}$

${\leadsto\displaystyle{ \sf Amount = \: 10000 \times \frac{1331}{1000} }}$

${\leadsto\displaystyle{ \sf Amount = \: 10 \cancel{000} \times \frac{1331}{10 \cancel{000}} }}$

${\leadsto\displaystyle{ \sf Amount =10 \times 1331 }}$

${\leadsto\displaystyle{ \sf Amount =Rs. \: 13310}} \: \bigstar$

Now, We know that :

${\leadsto{ \sf{Compound \: Interest = Amount - Principal}}}$

$\leadsto{ \sf{Compound \: Interest =13310 - 10000 }}$

$\leadsto{ \sf{Compound \: Interest = Rs. \: 3310}} \: \bigstar$

• Henceforth, Compound Interest is ₹3310.

${\large{\underline{\underline{\bf{Learn \: More\: : - }}}}}$

$\small\purple{\underline{\boxed{\bf{ Simple \: Interest = \dfrac{P \times R \times T}{100}}}}}$

$\small\purple{\underline{\boxed{\bf{Amount={P{\bigg(1 + \dfrac{R}{100}{\bigg)}^{T}}}}}}}$

$\small\purple{\underline{\boxed{\bf{Amount = Principle + Interest}}}}$

$\small\purple{\underline{\boxed{\bf{ Principle=Amount - Interest }}}}$

$\small\purple{\underline{\boxed{\bf{Principle = \dfrac{Amount\times 100 }{100 + (Time \times Rate)}}}}}$

$\small\purple{\underline{\boxed{\bf{Principle = \dfrac{Interest \times 100 }{Time \times Rate}}}}}$

$\small\purple{\underline{\boxed{\bf{Rate = \dfrac{Simple \: Interest \times 100}{Principle \times Time}}}}}$