Question

if the simple interest on a sum of money at 5% per annum for 4 years is rs.8000 find the compound interest on the same sum for the same period at the same rate compounded annually​

Answer 1

Step-by-step explanation:

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.

Hope it helps ❤️