Question

Principal = 5ooo
Rate=8
Duration:3 ​

Answer 1

Answer:

6298.56

6298.56C.I =A-P

6298.56C.I =A-P 6298.56 - 5000

6298.56C.I =A-P 6298.56 - 5000 = 1298.56

CI=1298.5

Answer 2

» Question :

If P = ₹ 5000 , Rate of interest = 8 % p.a and Time = 3 years ,then find :

1. Simple Interest
2. Compound interest
3. Difference Between simple and compound interest.

» To Find :

• Simple Interest

• Compound interest

• Compound interest Difference Between simple and compound interest.

» Given :

• Principal = ₹ 5000

• Time = 3 years

• Rate of interest = 8% p.a.

» We Know :

Simple Interest :

$\sf{\underline{\boxed{SI = \dfrac{P \times R \times t}{100}}}}$

Where,

• SI = Simple Interest
• P = Principal
• R = Rate of interest
• t = time

Amount Formula :

$\sf{\underline{\boxed{A = P\left(1 + \dfrac{R}{100}\right)^{n}}}}$

Where ,

• A = Amount
• P = Principal
• R = Rate of interest
• n = time period

Compound Interest :

$\sf{\underline{\boxed{CI = A - P}}}$

Where ,

• CI = Compound Interest
• A = Amount
• P = Principal

» Concept :

In the first two cases , we can find the answer only by substituting the values in it.

But in the third case , we have to Find the difference between the Compound Interest and the simple Interest.

» Solution :

Simple Interest :

We Know ,

• Principal = ₹ 5000

• Time = 3 years

• Rate of interest = 8% p.a.

Using the formula and Substituting the values in it ,we get :

$\sf{\underline{\boxed{SI = \dfrac{P \times R \times t}{100}}}}$

$\sf{\Rightarrow SI = \dfrac{5000 \times 8 \times 3}{100}}$

$\sf{\Rightarrow SI = \dfrac{50\cancel{00} \times 8 \times 3}{\cancel{100}}}$

$\sf{\Rightarrow SI = 50 \times 8 \times 3}$

$\sf{\Rightarrow SI = 1200}$

Hence, the simple Interest is ₹ 1200.

Compound Interest :

We Know ,

• Principal = ₹ 5000

• Time = 3 years

• Rate of interest = 8% p.a.

Using the Amount formula and Substituting the values in it ,we get :

$\sf{\underline{\boxed{A = P\left(1 + \dfrac{R}{100}\right)^{n}}}}$

$\sf{\Rightarrow A = 5000\left(1 + \dfrac{8}{100}\right)^{3}}$

$\sf{\Rightarrow A = 5000\left(\dfrac{100 + 8}{100}\right)^{3}}$

$\sf{\Rightarrow A = 5000\left(\dfrac{108}{100}\right)^{3}}$

$\sf{\Rightarrow A = 5000 \times \dfrac{108}{100} \times \dfrac{108}{100} \times \dfrac{108}{100}}$

$\sf{\Rightarrow A = 5\cancel{000} \times \dfrac{108}{\cancel{100}} \times \dfrac{108}{10\cancel{0}} \times \dfrac{108}{100}}$

$\sf{\Rightarrow A = 5 \times 108 \times \dfrac{\cancel{108}}{\cancel{10}} \times \dfrac{\cancel{108}}{\cancel{100}}}$

$\sf{\Rightarrow A = 5 \times 108 \times \dfrac{54}{5} \times \dfrac{54}{50}}$

$\sf{\Rightarrow A = \cancel{5} \times 108 \times \dfrac{54}{\cancel{5}} \times \dfrac{\cancel{54}}{\cancel{50}}}$

$\sf{\Rightarrow A = 108 \times 54 \times \dfrac{27}{25}}$

$\sf{\Rightarrow A = 6298.56}$

Thus, the amount is ₹6297.56.

Compound Interest = Amount - Principal

$\Rightarrow CI = 6297.56 - 5000$

$\Rightarrow CI = 1297.56$

Hence, the compound interest is ₹ 1297.56

Difference between CI and SI :

• Compound interest = ₹ 1297.56
• Simple Interest = ₹ 1200

Using the formula and Substituting the values in it,we get :

$\sf{\underline{\boxed{CI = A - P}}}$

$\sf{\Rightarrow CI = 1297.56 - 1200}$

$\sf{\Rightarrow CI = 97.56}$

Hence, the compound interest is ₹ 97.56.

Additional information :

• Amount (Compounded Half-yearly) =
• $\sf{A = P\left(1 + \dfrac{R}{200}\right)^{2n}}$

• Amount (Compounded quarterly) = $\sf{A = P\left(1 + \dfrac{R}{300}\right)^{3n}}$

• Amount for n no. of rate % = $\sf{A = P\left(1 + \dfrac{n_{1}}{300}\right)\left(1 + \dfrac{n_{2}}{300}\right).....}$