Question

what will be the compound interest of 3 years at 5% of the rate of 8000 rupess while interest is payable annually?
(A) 1150 Rupees (B) 1200 Rupees
(C)1250 Rupees (D) 1261 Rupees

Answer 1

Answer:

Given :-

• A sum of Rs 8000 for 3 years at the rate of 5% per annum while the interest is compounded annually.

To Find :-

• What is the compound interest.

Formula Used :-

$\clubsuit$ Amount Formula :

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

where,

• A = Amount
• P = Principal
• r = Rate of Interest
• n = Time Period

$\clubsuit$ Compound Interest Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{Compound\: Interest =\: A - P}}}\: \: \: \bigstar$

where,

• A = Amount
• P = Principal

Solution :-

First, we have to find the amount :

Given :

• Principal = Rs 8000
• Rate of Interest = 5% per annum
• Time Period = 3 years

According to the question by using the formula we get,

$\implies \bf A =\: P\bigg(1 + \dfrac{r}{100}\bigg)^n$

$\implies \sf A =\: 8000\bigg(1 + \dfrac{5}{100}\bigg)^3$

$\implies \sf A =\: 8000\bigg(\dfrac{105}{100}\bigg)$

$\implies \sf A =\: 8000\bigg(\dfrac{105}{100} \times \dfrac{105}{100} \times \dfrac{105}{100}\bigg)$

$\implies \sf A =\: 8000\bigg(\dfrac{1157625}{1000000}\bigg)$

$\implies \sf A =\: 8000 \times \dfrac{1157625}{1000000}$

$\implies \sf A =\: \dfrac{8000 \times 1157625}{1000000}$

$\implies \sf A =\: \dfrac{9261\cancel{000000}}{1\cancel{000000}}$

$\implies \sf A =\: \dfrac{9261}{1}$

$\implies \sf\bold{\purple{A =\: Rs\: 9261}}$

Hence, the amount is Rs 9261 .

Now, we have to find the compound interest :

Given :

• Amount = Rs 9261
• Principal = Rs 8000

According to the question by using the formula we get,

$\dashrightarrow \bf Compound\: Interest =\: A - P$

$\dashrightarrow \sf Compound\: Interest =\: Rs\: 9261 - Rs\: 8000$

$\dashrightarrow \sf\bold{\red{Compound\: Interest =\: Rs\: 1261}}$

$\therefore$ The compound interest is Rs 1261 .

Hence, the correct options is option no (D) 1261 .

Answer 2

Question:

What will be the compound interest of 3 years at 5% of the rate of 8000 rupess while interest is payable annually?

Given Options:

(A) 1150 Rupees

(B) 1200 Rupees

(C) 1250 Rupees

(D) 1261 Rupees

Answer:

(D) 1261 Rupees.

How To Get It:

There are three ways to find the answer of compound interest- 1) The long method where we find the compound interest year after year, 2) To find amount first and then difference between the amount and principal at the beginning to find the compound interest & 3) Direct finding compound interest.

I'm using option no. 3).

Formula:-

$\: \: \: \: \: \: \: \: CI = P[ (\frac{100 + R}{100}) ^{T} - 1]$

Where,

CI = Compound Interest

P = Principal

R = Rate

T = Time

Now,

$CI = P[ (\frac{100 + R}{100} )^{T} - 1]$

$\: \: \: \: \: \: \: \: =8000[ (\frac{100 + 5}{100} )^{3} - 1]$

$\: \: \: \: \: \: \: \: = 8000[ (\frac{105}{100} )^{3} - 1]$

$\: \: \: \: \: \: \: \: = 8000( \frac{1157625}{1000000} - 1)$

$\: \: \: \: \: \: \: \: = 8000( \frac{1157625 - 1000000}{1000000} )$

$\: \: \: \: \: \: \: \: = 8000 \times \frac{157625}{1000000}$

$\: \: \: \: \: \: \: \: =R s. \: 1261$

Therefore the required amount of compound interest is Rs. 1261 and Option (D) is the correct answer.

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