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Mathematics

Assertion (A): On ₹ 4,000, the simple interest in 3 years and at 5% p.a. is ₹ 600. The compound interest on the same sum at the same rate percent and at the end of second year will be ₹ 210.

Reason (R): For first year,

C.I. = S.I. for one year = ₹6003=₹200\dfrac{₹600}{3} = ₹200.

∴ C.I at the end of second year = ₹ 200 + interest of one year on ₹ 200.

  1. A is true, R is false.
  2. A is false, R is true.
  3. Both A and R are true.
  4. Both A and R are false.

Compound Interest

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Answer

Both A and R are true.

Explanation

Given,

Principal (P) = ₹ 4,000, Rate (R) = 5 % p.a., Time (T) = 3 years.

Simple interest, S.I. = P×R×T100\dfrac{P \times R \times T}{100}

S.I. = 4000×5×3100\dfrac{4000 \times 5 \times 3}{100}

= 40×1540 \times 15

= ₹ 600

Compound Interest for 2 years:

For the first year :

P = ₹ 4000, R = 5 % p.a., T = 1 year

C.I. = P×R×T100\dfrac{P \times R \times T}{100}

= 4000×5×1100\dfrac{4000 \times 5 \times 1}{100}

= ₹ 200

Amount at end of the first year = Principal + C.I.

= ₹ 4000 + ₹ 200

= ₹ 4200

For the second year :

P = ₹ 4200, R = 5 % p.a., T = 1 year

= 4200×5×1100\dfrac{4200 \times 5 \times 1}{100}

= ₹ 210

∴ Assertion (A) is true.

C.I. for first year = ₹ 200

S.I. for one year = ₹6003=₹200\dfrac{₹600}{3} = ₹200

∴ C.I. = S.I. for one year = ₹6003=₹200\dfrac{₹600}{3} = ₹200

The Interest for one year on ₹ 200 = PRT100\dfrac{PRT}{100}

= 200×5×1100\dfrac{200 \times 5 \times 1}{100}

= 1000100\dfrac{1000}{100}

= 10

Total C.I. at the end of the second year:

C.I. = ₹ 200 + ₹ 10 = ₹ 210

∴ C.I. at the end of the second year = ₹ 200 + interest for one year on ₹ 200.

∴ Reason (R) is true.

Hence, both Assertion (A) and Reason (R) are true.

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