Question

Rahul borrows ₹ 15,000 for 2 years at CI annually from a bank. After one year, it amounts to ₹ 16,200. Calculate (i) the rate of interest (ii) the interest for the second year.

Answer 1

We are given:

• Principal P = ₹ 15,000
• Time n = 2 years 
• Amount after 1 year A₁ = ₹ 16,200 
• Interest is compounded annually

Step 1: Find the rate of interest

Amount after 1 year formula (CI annually):

`A_1 = P(1 + r/100)`

Substitute the values:

`16,200 = 15,000 (1 + r/100)`

`1 + r/100 = (16,200)/(15,000) = 1.08`

`r/100 = 0.08`

`r = 8%`

Rate of interest = 8% p.a.

Step 2: Find the interest for the second year

• Amount at the end of 2nd year:
  `A_2 = A_1(1 + r/100)`
  = 16,200 × 1.08
  A₂ = 17,496
• CI for the second year:
  CI (2nd year) = A₂ – A₁
  = 17,496 – 16,200
  = 1,296

Interest for the second year = ₹ 1,296