Question

Find the amount and the compound interest on 2,000 at 5% per annum for 3 years.
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Answer 1

Answer:

Given :-

• A sum of Rs 2000 at 5% per annum for 3 years.

To Find :-

• What is the amount and compound interest.

Formula Used :-

$\clubsuit$ Amount Formula :

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

$\clubsuit$ Compound Interest or C.I Formula :

$\mapsto \sf\boxed{\bold{\pink{C.I =\: A - P}}}$

where,

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

Solution :-

First, we have to find the amount :

Given :

• Principal (P) = Rs 2000
• Rate of Interest (r) = 5%
• Time (t) = 3 years

According to the question by using the formula we get,

$\implies \sf A =\: 2000\bigg(1 + \dfrac{5}{100}\bigg)^3$

$\implies \sf A =\: 2000\bigg(\dfrac{100 + 5}{100}\bigg)^3$

$\implies \sf A =\: 2000\bigg(\dfrac{105}{100}\bigg)^3$

$\implies \sf A =\: 2{\cancel{0}}{\cancel{00}} \times \dfrac{105}{100} \times \dfrac{105}{10\cancel{0}} \times \dfrac{105}{1\cancel{00}}$

$\implies \sf A =\: \dfrac{2 \times 105 \times 105 \times 105}{1000}$

$\implies \sf A =\: \dfrac{231525\cancel{0}}{100\cancel{0}}$

$\implies \sf A =\: \dfrac{231525}{100}$

$\implies \sf\bold{\red{A =\: Rs\: 2315.25}}$

$\therefore$ The amount is Rs 2315.25.

Now, we have to find the compound interest or C.I :-

Given :

• Amount (A) = Rs 2315.25
• Principal (P) = Rs 2000

According to the question by using the formula we get,

$\longrightarrow \sf C.I = Rs\: 2315.25 - Rs\: 2000$

$\longrightarrow \sf C.I =\: Rs(2315.25 - 2000)$

$\longrightarrow \sf\bold{\red{C.I =\: Rs\: 315.25}}$

$\therefore$ The compound interest or C.I is Rs 315.25.

Answer 2

Solution :

• Find the amount and the compound interest on 2000 at 5% per annum for 3 years.

The principal here is Rs. 2000

Rate = 5% per annum

Time = 3 years.

Amount = Principal (1+r/100)^{time}

> Amount = 2000 × [ 1+5/100]^3

> Amount = 2000 × [ 1+1/20]^3

> Amount = 2000 × [ 20+1/20]^3

> Amount = 2000 × [21/20]^3

> Amount = 2000 × (21/20) × (21/20) × (21/20)

> Amount = 2000 × 9261/800

> 9261 × 20/8

> 185220/8

> 2315.25

Hence the amount is Rs. 2315.25

Compound interest = Amount - Principal

= 2315.25 - 2000

> 315.25

Answer : The amount and compound interest on the sum for 3 years are Rs. 2315.25 and Rs. 315.25 respectively .

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