Question

A sum of ₹8000 becomes ₹8400 in one year at a certain interest per annum. Find the compound interest on the same sum for two years at the same rate of Interest

Answer 1

Answer:

The Compound Interest is of Rs. 820.

Step-by-step explanation:

Given :

Principal = Rs. 8000

Amount = Rs. 8400

Time = 1 year

To find :

The compound interest on the same Principal at the same rate for 2 years.

Solution :

Rate -

Let the rate be R.

⇒ A = P(1 + R/100)ⁿ

⇒ 8400 = 8000 × (1 + R/100)¹

⇒ 8400/8000 = 100 + R/100

⇒ 1.05 = 100 + R/100

⇒ 1.05 × 100 = 100 + R

⇒ 105 = 100 + R

⇒ R = 105 - 100

⇒ R = 5

Rate = 5%

$\rule{300}{1.5}$

Compound interest -

⇒ CI = [P(1 + R/100)ⁿ] - P

⇒ CI = [8000 × (1 + 5/100)²] - 8000

⇒ CI = [8000 × (105/100)²] - 8000

⇒ CI = (8000 × 21/20 × 21/20) - 8000

⇒ CI = (20 × 21 × 21) - 8000

⇒ CI = 8820 - 8000

⇒ CI = 820

$\therefore$ The Compound Interest is of Rs. 820.

Answer 2

||✪✪ GIVEN ✪✪||

• Principal = Rs.8000
• Amount = Rs.8400

✯✯ To Find ✯✯

• compound interest on the same sum for two years at the same rate of Interest ?

|| ✰✰ ANSWER ✰✰ ||

Let Rate of interest is R% per annum.

→ SI = Amount - Principal .

→ SI = 8400 - 8000

→ SI = Rs.400

So,

→ R = (SI * 100) /(P * T)

Putting values ,

→ R = (400 * 100) / (8000 * 1)

→ R = 5% .

_____________________

Now, we have :-

→ Principal = 8000

→ Rate = 5 %

→ Time = 2 years.

So,

→ Amount = P[ 1 + (R/100) ]^T

Putting values,

→ Amount = 8000[ 1 + (5/100)]²

→ Amount = 8000[ 1 + (1/20)]²

→ Amount = 8000 (21/20)²

→ Amount = 8000 * (441/400)

→ Amount = Rs.8820 .

So,

→ Compound Interest = Amount - Principal

→ CI = 8820 - 8000

→ CI = Rs.820

Hence, The compound interest on the same sum for two years at the same rate of Interest is Rs.820.