Question

Assertion: When a sum is borrowed at 10% for 2 years compounded half-yearly, then `[A = P(1 + 10/100)^4]`.

Reason: When a sum is compounded half-yearly, the rate is halved and time is doubled.

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:

• Rate = 10% p.a.
• Time = 2 years
• Compounded half-yearly

Step 1: Check the assertion

For half-yearly compounding, the rate per half-year = `10/2` = 5%

The number of periods = 2 × 2 = 4 half-years

Correct formula for amount:

`A = P(1 + 5/100)^4`

= P(1.05)⁴

The given assertion uses 10% directly, which is wrong:

`A = P(1 + 10/100)^4`

= P(1.10)⁴

Assertion is false.

Step 2: Check the reason

“When a sum is compounded half-yearly, the rate is halved and time is doubled.” So the reason is true.