Question

4. Find the compound interest, correct to the
nearest rupee, on 2,400 for 2-
years at
5 percent per annum.
​

Answer 1

GiveN:-

• Principal = Rs.2400
• Rate = 5% per annum
• Time = 2 years

To FinD:-

The compound Interest.

SolutioN:-

We know that,

$\small{\green{\underline{\boxed{\bf{Compound\:Interest=\left[P\left(1+\dfrac{R}{100}\right)^n\right]-P}}}}}$

where,

• P is principal = Rs.2400
• R is rate = 5%
• n is time = 2 years

Putting the values,

$\small\implies{\sf{Compound\:Interest=\left[2400\left(1+\dfrac{5}{100}\right)^2\right]-2400}}$

$\small\implies{\sf{Compound\:Interest=\left[2400\left(1+\dfrac{\cancel{5}}{\cancel{100}}\right)^2\right]-2400}}$

$\small\implies{\sf{Compound\:Interest=\left[2400\left(1+\dfrac{1}{20}\right)^2\right]-2400}}$

$\small\implies{\sf{Compound\:Interest=\left[2400\left(\dfrac{20+1}{20}\right)^2\right]-2400}}$

$\small\implies{\sf{Compound\:Interest=\left[2400\left(\dfrac{21}{20}\right)^2\right]-2400}}$

$\small\implies{\sf{Compound\:Interest=\left[2400\left(\dfrac{21}{20}\times\dfrac{21}{20}\right)\right]-2400}}$

$\small\implies{\sf{Compound\:Interest=\left[2400\times\dfrac{21}{20}\times\dfrac{21}{20}\right]-2400}}$

$\small\implies{\sf{Compound\:Interest=\left[24\cancel{0}\cancel{0}\times\dfrac{21}{2\cancel{0}}\times\dfrac{21}{2\cancel{0}}\right]-2400}}$

$\small\implies{\sf{Compound\:Interest=\left[24\times\dfrac{21}{2}\times\dfrac{21}{2}\right]-2400}}$

$\small\implies{\sf{Compound\:Interest=\left[\cancel{24}\times\dfrac{21}{\cancel{2}}\times\dfrac{21}{2}\right]-2400}}$

$\small\implies{\sf{Compound\:Interest=\left[12\times21\times\dfrac{21}{2}\right]-2400}}$

$\small\implies{\sf{Compound\:Interest=\left[\cancel{12}\times21\times\dfrac{21}{\cancel{2}}\right]-2400}}$

$\small\implies{\sf{Compound\:Interest=\left[6\times21\times21\right]-2400}}$

$\small\implies{\sf{Compound\:Interest=2646-2400}}$

$\large\therefore\boxed{\bf{Compound\:Interest=Rs.246.}}$

• Rs.246 is the Compound Interest for 2 years.
• Now we have to find the interest for the ½ years

For that we have to use Simple Interest.

We know that,

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

where,

• Here is P i.e., principal is Rs.2646
• R is rate = 5%
• Time = ½ year

Putting the values,

$\small\implies{\sf{Simple\:Interest=\dfrac{2646\times5\times1}{100\times2}}}$

$\small\implies{\sf{Simple\:Interest=\dfrac{2646\times\cancel{5}\times1}{\cancel{100}\times2}}}$

$\small\implies{\sf{Simple\:Interest=\dfrac{2646\times1}{20\times2}}}$

$\small\implies{\sf{Simple\:Interest=\dfrac{\cancel{2646}\times1}{20\times\cancel{2}}}}$

$\small\implies{\sf{Simple\:Interest=\dfrac{1323\times1}{20}}}$

$\small\implies{\sf{Simple\:Interest=\dfrac{1323}{20}}}$

$\large\therefore\boxed{\bf{Simple\:Interest=Rs.66.15}}$

Now we have to add the compound interest and the simple interest,

$\small\implies{\sf{Interest=Rs(246+66.15)}}$

$\small\implies{\sf{Interest=Rs.312.15}}$

It is said correct to nearest rupees,

So,

$\large\therefore\boxed{\bf{Compound\:Interest=Rs.312.}}$

Compound Interest for 2½ years is Rs.312.

Answer 2

$\huge \sf \underline \red{Answer : }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ \boxed{ \underline{ \underline{ \purple{ \tt{ = 312 \: }}}}}}$

$\huge \sf \underline \blue{Given : }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ \star \:principal = 2400}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ \star \:time = 2years}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ \star \:rate = 5\%}$

$\sf \underline{we \: know \: that \: formula : }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ \boxed{ \underline{ \underline{ \red{ \tt{A = 1 + \dfrac{r}{100} {}^{2}} \: }}}}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ = 2400(1 + \dfrac{5}{100} {}^{2})}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ = 2400( \dfrac{105}{100}} {)}^{2}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ = \dfrac{2400 \times 105 \times 105 }{100 \times100 }}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ RS = 2646}$

$\sf{so}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \underline \red{interest = A - P}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \underline{ = 2646 - 2400}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \underline{ = 246}$

_____________________________________

$\: \: \: \: \: \sf \underline{After \: next \: \dfrac{1}{2} year}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ \star \:principal = 2646}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ \star \:time = \dfrac{1}{2} years}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ \star \:rate = 5\%}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ \boxed{ \underline{ \underline{ \red{ \tt{i = \dfrac{ptr}{100} \: }}}}}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ = \dfrac{2646 \times 1 \times 5}{2 \times 100} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ RS = 66.15}$

_____________________________________

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \underline{ \: total \: interest = 246 + 66.15}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf { = 312.15}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf { = 312}$