Question

find amount and the compound interest. P = 15000. N = 2. R = 15. A = ? , I = ?​

Answer 1

Answer :-

• Simple interest = Rs. 4,500
• The amount = Rs. 19,837.5
• Compund interest = Rs. 4,837.5

Step-by-step Explanation:

To Find: The amount, compound interest and simple interest.

Given: P = Rs. 15,000; n = 2 years; Rate = 15%

Calculating simple interest:

As we know that,

Simple interest = PRT/100

Where,

• P = Principal
• R = Rate
• T = Time.

→ PRT/100

→ P*R*T/100

→ (15,000 × 15 × 2)/100 ... dividing 15,000 by 100

→ 150 × 15 × 2

→ Rs. 4,500 = Simple interest

Now, Calculating amount :-

As we know that,

Amount = P(1 + r/100)ⁿ

Where,

• P = Principal
• r = Rate
• ⁿ = Time.

→ P(1 + r/100)ⁿ

→ 15,000(1 + 15/100)²

→ 15,000(1 + 3/20)²

→ 15,000(23/20)²

→ 15,000 × 23/20 × 23/20

→ 1,500 × 23/2 × 23/20

→ 150 × 23/2 × 23/2

→ Rs. 19,837.5 = Amount

Calculating the compound interest:

As we know that,

Compound interest = Amount - Principal

→ Amount - Principal

→ Rs. 19,837.5 - Rs. 15,000

→ Rs. 4,837.5

Formula used :-

• Simple interest = PRT/100
• Amount = P(1 + r/100)ⁿ
• Compound interest = A - P

Where,

P = Principal

R = Rate

T & ⁿ = Time

R & r = Rate

A = Amount.

Answer 2

Given :-

P = 15,000

N = 2 years

R = 15 %

To find :-

Amount and compound interest.

Explanation :-

As we know that,

$\boxed{ \tt \: A\: =P \bigg(1 + \frac{r}{100} \bigg) {}^{n} }$

where,

A = Amount

P = principle

r = rate

n = time

Substituting the values,

$\tt \: A= 15000 \bigg(1 + \dfrac{15}{100} \bigg) {}^{2}$

$\tt \: A = 15000 \bigg(1 + \dfrac{3}{20} \bigg) {}^{2}$

$\tt \: A = 15000 \bigg( \dfrac{23}{20} \bigg) {}^{2}$

$\tt \: A = 150 \not0 \not0 \bigg( \dfrac{23 \times 23}{2 \not0 \times 2 \not0} \bigg)$

$\tt \: A = \cancel{150 } \tiny{75}\bigg( \large \dfrac{23 \times 23}{ \cancel4 \: \tiny{2}} \bigg)$

$\tt \: A= \dfrac{75 \times 529}{2}$

$\tt \: A = \bigg( \dfrac{39675}{2} \bigg)$

$\: \: \: \boxed{ \tt \: A = 19837.5} \bigstar$

So, Amount is 19,837.5 Rs

Also we know that,

Compound interest (C.I) = A-P

$\tt \: C.I = 19837.5 - 15000$

$\: \: \boxed{ \tt \: C.I = 4837.5} \bigstar$

So, Compound interest is 4837.5 Rs

Also, we know that,

$\boxed{\tt{S.I} = \dfrac{PTR}{100}}$

where,

S.I = simple interest

P = principal

T = time

R = rate

Substituting the values,

$\tt{S.I} = \dfrac{15,000\times 2\times 15}{100}$

$\tt{S.I} = \dfrac{150\times 2\times 15}{1}$

$\tt{S.I} = {300\times 15}$

$\: \: \boxed{ \tt \: S.I= 4500 Rs} \bigstar$