Question

1. A sum invested at 10% p.a. compound interest amounts to ₹ 5445 in 2 years. If interest is compounded
annually, what is the sum invested?​

Answer 1

Step-by-step explanation:

Given:-

• Rate of Interest = 10%

• Amount = Rs. 5445

• Time = 2 years

• And the Interest is compounded annually.

To Find:-

• The sum invested (Principal)

Solution:-

Let the sum of money invested be ' P '

As we know that:-

The formula used for finding Amount is

$\boxed{ \sf \bull \: Amount = P \bigg(1 + \frac{r}{100} \bigg)^{n} }$

Here:-

• Amount = Rs.5445

• P = Principal = ?

• r = Rate of Interest = 10%

• n = time = 2 years

Substituting the values:-

$\sf \implies 5445 = P \times \bigg(1 + \dfrac{10}{100} \bigg)^{2}$

$\sf \implies 5445 = P\times \bigg(\dfrac{100 + 10}{100} \bigg)^{2}$

$\sf \implies 5445 = P\times \bigg(\dfrac{110}{100} \bigg)^{2}$

$\sf \implies 5445 = P\times \bigg(\dfrac{11}{10} \bigg)^{2}$

$\sf \implies 5445 = P\times \dfrac{11 \times 11}{10 \times 10}$

$\sf \implies 5445 = P\times \dfrac{121}{100}$

$\sf \implies P = 5445\times \dfrac{100}{121}$

$\sf \implies P = 45\times 100$

$\sf \implies P = 4500$

$\underline{\boxed{\sf \therefore The \: sum \: invested\: (Principal) = Rs.4500}}$

Answer 2

$\huge{\boxed{\rm{\purple{Question}}}}$

A sum invested at 10% p.a. compound interest amounts to ₹ 5445 in 2 years. If interest is compounded annually, what is the sum invested?

$\huge{\boxed{\rm{\purple{Answer}}}}$

${\bigstar}\large{\boxed{\sf{\green{Given \: that}}}}$

• Rate of interest = 10%
• The interest is compounded annually
• Amount = ₹5445
• Time = 2 years

${\bigstar}\large{\boxed{\sf{\green{To \: find}}}}$

• Principal

${\bigstar}\large{\boxed{\sf{\green{Solution}}}}$

Let Principal as “P”.

As we know that,

Formula to finding amount is -

Amount = ( 1 + r/100^n )

Here,

• Amount = ₹ 5445
• Principal = P
• Rate of interest = 10%
• Time = 10 year's

Substituting the value,

• 5445 = P × ( 1+ 10/100 )²
• 5445 = P × ( 100 + 10/100 )²
• 5445 = P × ( 110 /100 )²
• 5445 = P × ( 11 /10 )²
• 5445 = P × ( 11 × 11 / 10 × 10 )
• 5445 = P × 121 / 100
• P = 5445 × 100 / 121
• P = 45 × 100
• P = 4500

Answer = 4500

Hence, Principal = 4500

@Itzbeautyqueen23

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