Question

13. A sum of Rs 8,000 becomes Rs 8,400 in one year at a certain interest rate per annum. Find th
compound interest on the sum for 2 years at the same rate of interest.
​

Answer 1

Answer:

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.