Question

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Answer 1

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Compound Interest = ₹ 331.

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GIVEN :

• Simple interest = ₹ 300
• Time = 3 years
• Rate of interest = 10%

TO FIND :

• Compound interest

SOLUTION :

First we will calculate the principal amount.

For this we have the formula for simple interest.

Formula :

$\bold{\large{\boxed{\sf{\red{S.I\:=\:{\dfrac{P\times\:R\times\:T}{100}}}}}}}$

Where,

• SI = Simple Interest
• P = Principal Amount
• R = Rate of interest
• T = time period

Block in the values,

$\rightarrow$ $\bold{300\:=\:{\dfrac{P\times\:10\times\:3}{100}}}$

$\rightarrow$ $\bold{300\:=\:{\dfrac{P\times\:30}{100}}}$

$\rightarrow$ $\bold{\dfrac{300\:\times\:100=\:P\times\:30}}$

$\rightarrow$ $\bold{30000\:=\:P\:\times\:30}$

$\rightarrow$ $\bold{\dfrac{30000}{30}}$ = P

$\rightarrow$ $\bold{1000=P}$

•°• Principal amount = ₹ 1000

Now we will find amount, A.

Formula :

$\bold{\large{\boxed{\sf{\green{A\:=\:P\:(1\:+\:{\dfrac{r}{100})^n}}}}}}$

Where,

• A = amount
• P = principal amount
• r = rate of interest
• n = time period

Block in the values,

$\rightarrow$ $\bold{A\:=\:1000\:(1+{\dfrac{10}{100}})^3}$

$\rightarrow$ $\bold{A\:=\:1000\:({\dfrac{100+10}{100}})^3}$

$\rightarrow$ $\bold{A\:=\:1000\:({\dfrac{110}{100}})^3}$

$\rightarrow$ $\bold{A=\:1000\times\:{\dfrac{110}{100}\times\:{\dfrac{110}{100}\times\:{\dfrac{110}{100}}}}}$

$\rightarrow$ $\bold{A\:=\:{\dfrac{1331000000}{1000000}}}$

$\rightarrow$ $\bold{A=\:1331}$

•°• Amount = ₹ 1331

Now we can calculate the compound interest by simply calculating the difference between Amount and principal.

Formula :

CI = Amount - Principal

Block in the values,

$\rightarrow$ $\bold{CI\:=\:1331-1000}$

$\rightarrow$ $\bold{CI\:=\:331}$

•°• Compound interest for 3 years will be ₹ 331.

Answer 2

SOLUTION:-

════════════

Given:

The simple interest on a certain principal for 3 years at 10% p.a. is Rs.300.

To find:

══════

The compound Interest accrued in 3 years.

Explanation:

═════════

In first Case:

• Simple Interest= Rs.300
• Time= 3 years
• Rate= 10% p.a.
• Principal= ___?

Formula of Simple Interest:

════════════════════

$S.I. = \frac{P \times R \times T}{ 100 }$

So,

Formula of the Principal:

$P = \frac{S.I. \times 100}{R \times T}$

According to the question:

═════════════════

$P = \frac{300 \times 100}{3 \times 10} \\ \\ P = \frac{30000}{30} \\ \\ P = Rs.1000$

&

In second Case:

We have,

• Principal= Rs.1000
• Rate = 10%
• Time= 3 years

Here,find Amount of Compound Interest

Formula of the compound Interest:

══════════════════════

C.I.= Amount - Principal

Or

$A = P(1 + \frac{R}{100} ) {}^{n}$

So,

$A= 1000(1 + \frac{10}{100} ) {}^{3} \\ \\ A = 1000(1 + \frac{1}{10} ) {}^{3} \\ \\ A = 1000( \frac{10 + 1}{10} ) {}^{3} \\ \\ A = 1000 \times \frac{11}{10} \times \frac{11}{10} \times \frac{11}{10} \\ \\ A = (11) {}^{3} \\ \\ A = Rs.1331$

Now,

Compound Interest:

═════════════

Amount - Principal

Rs.1331 - Rs.1000

Rs.331

Hence,

The compound Interest accrued in 3 years is Rs.331

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