Assertion (A): At compound Interest for 5th year = Interest in 5 years - Interest in 4 years

Reason (R): Interest of 5th year = Amount in 5 years - Amount in 4 years

1. A is true, but R is false.

2. A is false, but R is true.

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

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

Let ₹ P be the principal amount, R be the rate of interest and n be time.

We know that,

⇒ C.I. = Amount - Principal

As we know that Principal of 5th year = Amount of 4th year

⇒ C.I.₅ = A₅ - A₄

⇒ Interest of 5th year = Amount in 5 years - Amount in 4 years

So, reason (R) is true.

Thus, proved

⇒ Interest for 5th year = Amount in 5 years - Amount in 4 years

⇒ Interest for 5th year = P + Interest in 5 years - (P + Interest in 4 years)

⇒ Interest for 5th year = Interest in 5 years - Interest in 4 years

So, assertion (A) is true.

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

Hence, option 3 is correct option.