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Mathematics

Joseph has a recurring deposit account in a bank for two years at the rate of 8\% per annum simple interest.

If the monthly instalment is ₹100 and the rate of interest is 8\%, in how many months Joseph will receive ₹52 as interest?

  1. 18

  2. 30

  3. 12

  4. 6

Banking

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Answer

Given:

I = ₹52

P = ₹100

r = 8\%

I=P×n(n+1)2×12×R100∴I=100×n(n+1)2×12×810052=n(n+1)24×852=n(n+1)3n(n+1)=52×3n(n+1)=156n2+n−156=0n2+13n−12n−156=0n(n+13)−12(n+13)=0(n+13)(n−12)=0n=−13 or n=12I = P \times \dfrac{n(n+1)}{2 \times 12} \times \dfrac{R}{100} \\[1em] \therefore I = 100 \times \dfrac{n(n+1)}{2 \times 12} \times \dfrac{8}{100} \\[1em] 52 = \dfrac{n(n+1)}{24}\times 8 \\[1em] 52 = \dfrac{n(n+1)}{3} \\[1em] n(n+1) =52 \times 3 \\[1em] n(n+1) = 156 \\[1em] n^2+n-156 = 0 \\[1em] n^2+13n - 12n-156 = 0 \\[1em] n(n+13) - 12(n+13) = 0 \\[1em] (n+13)(n-12) = 0 \\[1em] n=-13 \text{ or } n=12

Since the number of months cannot be negative.

∴ n = 12 months

Hence, Option 3 is the correct option.

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