Question

the difference between the compound interest compounded annually and simple interest on the certain sum at rate of 6% per annum for 2 years is 54 find the sum​

Answer 1

S O L U T I O N :

$\underline{\bf{Given\::}}$

• Rate, (R) = 6% p.a
• Time, (n) = 2 years
• Difference = 54

$\underline{\bf{Explanation\::}}$

As we know that formula of the compound interest & simple Interest;

$\boxed{\bf{C.I= P\bigg(1+\frac{R}{100} \bigg)^{n}- P}}$

$\boxed{\bf{S.I = \frac{PRT}{100} }}$

A/q

$\mapsto\tt{\Bigg[P\bigg(1 + \dfrac{R}{100} \bigg)^{n} - P \Bigg] - \Bigg[\dfrac{PRT}{100} \Bigg] = 54}$

$\mapsto\tt{\Bigg[P\bigg(1 + \dfrac{6}{100} \bigg)^{2} - P \Bigg] - \Bigg[\dfrac{P\times 6\times 2}{100} \Bigg] = 54}$

$\mapsto\tt{\Bigg[P\bigg(1 + \cancel{\dfrac{6}{100}} \bigg)^{2} - P \Bigg] - \Bigg[\dfrac{P\times 6\times 2}{100} \Bigg] = 54}$

$\mapsto\tt{\Bigg[P\bigg(1 + \dfrac{3}{50} \bigg)^{2} - P \Bigg] - \Bigg[\dfrac{12P}{100} \Bigg] = 54}$

$\mapsto\tt{\Bigg[P\bigg( \dfrac{50+3}{50} \bigg)^{2} - P \Bigg] - \Bigg[\dfrac{12P}{100} \Bigg] = 54}$

$\mapsto\tt{\Bigg[P\bigg( \dfrac{53}{50} \bigg)^{2} - P \Bigg] - \Bigg[\dfrac{12P}{100} \Bigg] = 54}$

$\mapsto\tt{\Bigg[P \times \bigg(\dfrac{2809}{2500}\bigg) - P \Bigg] - \Bigg[\dfrac{12P}{100} \Bigg] = 54}$

$\mapsto\tt{\Bigg[ \dfrac{2809P}{2500} - P \Bigg] - \Bigg[\dfrac{12P}{100} \Bigg] = 54}$

$\mapsto\tt{\Bigg[ \dfrac{2809P - 2500P}{2500} \Bigg] - \Bigg[\dfrac{12P}{100} \Bigg] = 54}$

$\mapsto\tt{\Bigg[ \dfrac{309P}{2500} \Bigg] - \Bigg[\dfrac{12P}{100} \Bigg] = 54}$

$\mapsto\tt{ \dfrac{309P}{2500} - \dfrac{12P}{100} = 54}$

$\mapsto\tt{ \dfrac{309P - 300P}{2500} = 54}$

$\mapsto\tt{ \dfrac{9P}{2500} = 54}$

$\mapsto\tt{ 9P = 54 \times 2500}$

$\mapsto\tt{ 9P = 135000}$

$\mapsto\tt{ P = \cancel{135000/9}}$

$\mapsto\bf{P = Rs.15000}$

Thus,

The sum will be Rs.15000 .

Answer 2

$\huge{\boxed{\bf{Hola!}}}$

GIVEN THAT:-

➱COMPOUND INTEREST - SIMPLE

➱INTEREST=54

➱PRINCIPAL=P

➱RATE%=6%

➱TIME=2 YEARS

NOW,

COMPOUND INTEREST-SIMPLE INTEREST=54

➱{[P(1+R/100]-P}-PRT/100=54

➱{[P(1+6/100)-P)-P*6*2/100=54

➱{[P(106/100)1-P)-P*3/25=54

➱(106P-100P/100J-3P/25=54

➱6P/100-3P/25=54

➱6P-12P/100=54

➱-6P /100=54

➱-6P=54*100

➱-P=54*100/6

➱-P=900

➱P=-900

$\huge{\fcolorbox{a}{blue}{\fcolorbox{aqua}{aqua}{hope it helps you}}}$