Q) Kavita has given time deposit in her bank. She deposited Rs. 600 per month and gets Rs. 6,165 at the time of maturity. If Rate of interest is 6% per annum, find total time for which account was held.

Ans: Given that:

Maturity value of RD account = Rs. 6, 165 (given)

Monthly instalment, P = Rs. 600 (given)

Rate of Interest = 6%

Step 1: Let’s consider the number of months be ‘n’

∴ Total investment = n x P = n x 600 = 600 n

Step 2: Interest Amount, I = P ×

= 600 ×

= × n (n + 1)

Step 3: We know that, Maturity value of RD account = Total investment + Interest Amount

∴ 6165 = 600 n + × n (n + 1)

∴ 6165 x 2 = 1200 n + 3 (n² + n)

∴ 12330 = 1200 n + 3 n² + 3 n

∴ 3 n² + 1203 n – 12330 = 0

∴ n² + 401 n – 4110 = 0

∴ n² + 411 n – 10 n – 4110 = 0

∴ n (n + 411) – 10 (n + 411) = 0

∴ (n + 411) (n – 10) = 0

∴ n = 10 and n = – 411

Here, we reject n = – 411 because months value can not be negative, hence n = 10

Hence time period of RD account is 10 months.

Check: If Monthly Instalment value is 600, then money invested over 10 months = 10 x 600 = 6000

Interest earned = P ×

= 600 x = 165

Total maturity amount = 6000 + 165 = 6165

Since this amount matches with given maturity amount, our answer is correct.

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