Question

Ravi and Gaurav both land 20000 each other to their friends for 24 months Ravi charge a compound interest of 20% compound annually whereas Gaurav charge at the same interest rate but compounded half yearly who received more money at the end of 24 months and by how much

Answer 1

Answer:

Formulas to be used:

$\text{Compound interest compounded yearly} = P [ 1+ \dfrac{R}{100} ]^T\\\\\\\text{Compound Interest Compounded half-yearly} = P [ 1 + \dfrac{R}{200} ]^{2T}$

According to the question,

• P = 20,000
• T = 2 years
• R = 20%

Case 1: Compounding Interest Yearly ( Ravi )

Substituting the values in the formula we get,

$\implies A = 20,000 \times [ 1 + \dfrac{20}{100} ]^2\\\\\implies A = 20,000 \times [ 1 + 0.2 ]^2\\\\\implies A = 20,000 \times 1.44 \\\\\implies A = Rs.\: 28,800$

Case 2: Compounding Interest Half Yearly ( Gaurav )

Substituting the values we get,

$\implies A = 20,000 \times [ 1 + \dfrac{20}{200} ]^4\\\\\implies A = 20,000 \times [ 1 + 0.1 ]^4\\\\\implies A = 20,000 \times 1.4\\\\\implies A = Rs.\:29,282$

Therefore Gaurav received the highest amount after 24 months by a gain of Rs. 482 more than Gaurav.

Answer 2

Question :

Ravi and Gaurav both lend Rs 20,000 each other to their friends for 24 months, Ravi charge a compound interest of 20% compound annually whereas Gaurav charge at the same interest rate but compounded half yearly, who received more money at the end of 24 months and by how much?

Solution :

$\rule {197}{1}$

$\underline {\bold {In\:First\:case: }}$

$\boxed {\purple{A=P{( 1+ \frac{R}{100} )} ^{T} }}$

$\implies A=P{( 1+ \frac{R}{100} )} ^{T} \\\\ \implies A=Rs \: 20,000{(1 + \frac{20}{100} )} ^{T} \\\\ \implies A=Rs \: 20,000{(1 + \frac{1}{5} )} ^{2} \\\\ \implies A = Rs \: 20,000{( \frac{5 + 1}{5} )}^{2} \\\\ \implies A= Rs \: 20,000 \times \frac{6}{ 5} \times \frac{6}{5} \\\\\implies A= Rs \: (800 \times 6 \times 6) \\\\\implies A= Rs \: 28,800$

$\therefore {Amount\: received \:by \:Ravi\:is\:Rs \: 28,800.}$

$\rule {197}{1}$

$\underline {\bold {In\:second\:case: }}$

$\boxed {\purple{A=P{( 1+ \frac{R}{200} )} ^{2T} }}$

$\implies A=P{( 1+ \frac{R}{200} )} ^{2T} \\\\ \implies A=Rs \: 20,000{( 1+ \frac{20}{200} )} ^{2 \times 2}\\\\ \implies A=Rs \: 20,000{( 1+ \frac{1}{10} )} ^{4} \\\\ \implies A=Rs \: 20,000{( \frac{10 + 1}{4} )} ^{4} \\\\ \implies A=Rs \: 20,000 \times \frac{11}{10} \times \frac{11}{10} \times \frac{11}{10} \times \frac{11}{10} \\\\ \implies A=Rs \: (2 \times 11 \times 11 \times 11 \times 11) \\\\ \implies A=Rs \:29,282$

$\therefore {Amount\: received \:by \:Gaurav \:is\:Rs \: 29,282.}$

$\rule {197}{2}$

$\therefore {\green{Gaurav \:received\: more\:money\:by \:Rs\:(29,282-28,800)= Rs\:482.}}$