**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 (n^{2} + n)

∴ 12330 = 1200 n + 3 n^{2} + 3 n

∴ 3 n^{2} + 1203 n – 12330 = 0

∴ n^{2 }+ 401 n – 4110 = 0

∴ n^{2} + 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.*

**Please press the “Heart”, if you liked the solution.**