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Mathematics

Jena has a cumulative deposit account in Indian Bank. She deposit ₹ 500 per month for 2 years. Bank pays interest at the rate of 6% p.a.

Assertion (A): Money received by Jena at maturity is ₹ 12,750.

Reason (R): Maturity value = money deposit + interest.

  1. Assertion (A) is true, but Reason (R) is false.

  2. Assertion (A) is false, but Reason (R) is true.

  3. Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).

  4. Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).

Banking

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Answer

Given,

P = ₹ 500/month

n = 2 years or 24 months

r% = 6%

By formula,

M.V. = money deposit + interest

So, reason (R) is true.

M.V. = P x n + P x n(n + 1)2×12×r100\dfrac{\text{n(n + 1)}}{2 \times 12} \times \dfrac{\text{r}}{100}

Substituting the values, we get :

M.V.=500×24+500×24(24+1)2×12×6100=1200+500×24×2524×6100=1200+500×25×6100=1200+500×64=1200+125×6=1200+750=12,750M.V. = 500 \times 24 + 500 \times \dfrac{24(24 + 1)}{2 \times 12} \times \dfrac{6}{100}\\[1em] = 1200 + 500 \times \dfrac{24 \times 25}{24} \times \dfrac{6}{100}\\[1em] = 1200 + 500 \times 25 \times \dfrac{6}{100}\\[1em] = 1200 + 500 \times \dfrac{6}{4}\\[1em] = 1200 + 125 \times 6\\[1em] = 1200 + 750\\[1em] = ₹ 12,750

So, both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).

Hence, option 3 is the correct option.

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