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Mathematics

Rohana has a recurring deposit account in State Bank of India. She deposits ₹ 800 per month for 2122\dfrac{1}{2} years. Bank pays interest at the rate of 5% p.a.

Assertion (A): Interest earned by Rohana in 2122\dfrac{1}{2} years is ₹ 1,650.

Reason (R): Interest earned = P×n(n + 1)2×12×r100P \times \dfrac{\text{n(n + 1)}}{2 \times 12} \times \dfrac{\text{r}}{100}

where, P = monthly instalment, n = number of installments and r = rate of interest p.a.

  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).

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Answer

Given,

P = ₹ 800/month

n = 2122\dfrac{1}{2} years or 30 months

r% = 5%

By formula,

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

So, reason (R) is true.

Substituting the values, we get :

I=800×30(30+1)2×12×5100=800×30×3124×5100=800×10×318×5100=10×31×5=₹1,550.I = 800 \times \dfrac{30(30 + 1)}{2 \times 12} \times \dfrac{5}{100}\\[1em] = 800 \times \dfrac{30 \times 31}{24} \times \dfrac{5}{100}\\[1em] = 800 \times \dfrac{10 \times 31}{8} \times \dfrac{5}{100}\\[1em] = 10 \times 31 \times 5\\[1em] = ₹ 1,550.

So, assertion (A) is false.

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

Hence, option 2 is the correct option.

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