Question

The difference between the compound interest and simple interest on a sum of money at 6% p.a for a period of 2 years is RS. 54 if the interest is compounded annually find the sum. ​

Answer 1

Answer:

The sum of money is Rs. 15,000.

Step-by-step explanation:

Given :

Difference between the Compound Interest and Simple Interest = Rs. 54

At rate = 6% p.a

Time = 2 years

To find :

The sum of money

Solution :

✯ $\textsf{\underline{\underline{Simple Interest -}}}$

• Rate = 6%
• Time = 2 years
• Principal = P

$\bigstar \: \boxed{\tt{SI = \frac{Principal \times Rate \times Time}{100}}}$

$\tt{\longrightarrow} \:SI = \dfrac{P \times 6 \times 2}{100} \\ \\ \tt{\longrightarrow} \:SI = \frac{12P}{100}$

$\rule{300}{1.5}$

✯ $\textsf{\underline{\underline{Compound Interest -}}}$

$\bigstar \: {\boxed{\tt{CI= P\left( 1 + \frac{R}{100}\right)^{N}} -P }}$

$\tt{\longrightarrow} \: {CI= P\left( 1 + \dfrac{6}{100}\right)^{2}} -1 \\ \\ \tt{\longrightarrow} \: {CI=P\left(\dfrac{106}{100}\right)^{2}} -1\\ \\ \tt{\longrightarrow} \: {CI=P\left(\dfrac{53}{50}\right)^{2}} -1 \\ \\ \tt{\longrightarrow} \: {CI=P \times \frac{2809}{2500} -1} \\ \\ \tt{\longrightarrow} \: {CI= \frac{309P}{100}}$

$\rule{300}{1.5}$

$\textsf{\underline{\underline{Difference between the CI and SI}}}$

Compound Interest = $\tt{\frac{309P}{100}}$

Simple Interest = $\tt{\frac{12P}{100}}$

$\tt{\longrightarrow} \: \dfrac{309P}{2500} - \dfrac{12P}{100} = 54 \\ \\ \tt{\longrightarrow} \: \dfrac{309P - 300P}{2500} = 54 \\ \\ \tt{\longrightarrow} \: \dfrac{9P}{2500} = 54 \\ \\ \tt{\longrightarrow} \: 9P = 54 \times 2500 \\ \\ \tt{\longrightarrow} \: 9P = 135000 \\ \\ \tt{\longrightarrow} \: P = \dfrac{135000}{9} \\ \\ \tt{\longrightarrow} \: P = 15000$

Principal = Rs. 15,000

$\therefore$ The sum of money is Rs. 15,000.

Answer 2

$\huge\pink{Answer}$

The sum of money = Rs. 15,000

Given :

Difference between the compound interest and simple interest = Rs. 54

At rate = 6 °/• p.a

Time = 2 years

Find = Sum of money

Solution:

◇◇Simple interest ◇◇

• Rate = 6 percent
• Time = 2 years
• Principal = p

◇◇ SI = principal × rate × time ◇◇

100

------> SI = p × 6 × 2 ◇◇

100

------> SI = 12p ◇◇

100

_____________◇_______________

◇◇Compound interest ◇◇

CI = P ( 1+\frac{6}{100})r{}^{2} -1

$(\frac{106}{100}^{2} - 1$