Question

Assertion: Compound Interest for the second year on ₹ 8000 at 15% p.a is ₹ 1380.

Reason: Simple Interest and Compound Interest are same for the first year.

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

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

Explanation:

Given:

• Principal P = ₹ 8000
• Rate r = 15% p.a.
• Compound Interest (CI) for the second year = ₹ 1380? 
• Reason: Simple Interest (SI) and Compound Interest (CI) are the same for the first year.

Step 1: Check if the assertion is true

CI for the second year formula:

CI for 2nd year = `P xx r xx (1 + r/100)^(1/100)`

Or equivalently:

Amount at the end of 1 year:

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

A₁ = 8000 × 1.15

A₁ = 9200

Amount at the end of 2 years:

A₂ = 9200 × 1.15

A₂ = 10,580

CI for second year = A₂ – A₁

CI for second year = 10580 – 9200

CI for second year = 1380

Step 2: Check if the reason is true

For the first year, CI is calculated on principal only:

CI for 1st year = `(P xx r)/100`

= `(8000 xx 15)/100`

= 1200

SI for 1 year = `(P xx r xx 1)/100` = 1200

SI and CI are the same for the first year.

Step 3: Check if the reason correctly explains the assertion

• Assertion: CI for second year = 1380
• Reason: SI and CI are same for the first year

The fact that CI = SI in the first year does not explain why the Cl for the second year is 1380. The second-year CI is higher because of interest on interest, not because of the first-year equality.