Question

Assertion: The Compound Interest on ₹ 8000 for the second year is ₹ 1680 at 10% p.a., calculated annually.

Reason: `[CI = P(1 + r/100)^n - P]`

Options

• Both A and R are true and R is the correct reason for A.

• Both A and R are true but R is the incorrect reason for A.

• A is true but R is false.

• A is false but R is true.

Answer 1

A is false but R is true.

Explanation:

Given:

• Principal P = ₹ 8000
• Rate r = 10% p.a.
• Time = 2 years (we are asked for second year CI)
• Compounding annually

Step 1: Find the CI for the second year

• Step 1a: Amount at the end of 1 year:
  `A_1 = P(1 + r/100) = 8000 xx 1.10 = 8800`

• Step 1b: Amount at the end of 2 years:
  A₂ = 8800 × 1.10 = 9680

• Step 1c: CI for second year:
  CI for 2nd year = A₂ – A₁
  = 9680 – 8800
  = 880

Assertion says ₹ 1680 → False

Step 2: Check the reason

• Reason formula:
  CI for n years = `P(1 + r/100)^n - P`

Reason is true