**Q) The maturity value of a R.D account is Rs. 16,176. If monthly investment is Rs. 400 and the rate of interest is 8%, find the time (period) of this R.D. Account.**

**Ans: **Given that:

Monthly Instalment, P = Rs. 400

Rate of Interest, r = 8 %

Maturity value of RD account = Rs. 16, 176

**Step 1:** Let’s consider the time period is n months

We know that Interest Amount, I = P ×

= 400 ×

= × n (n + 1)

**Step 2:** Since, Monthly instalment, P = Rs. 400 (given)

and Number of months invested = n

∴ Total investment = n x P = n x 400 = 400 n

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

∴ 16176 = 400 n + × n (n + 1)

∴ 16176 x 3 = 400 n x 3 + 4 (n ^{2} + n)

∴ 48528 = 1200 n + 4 n ^{2} + 4n

∴ 4 n ^{2} + 1204 n – 48528 = 0

∴ n ^{2} + 301 n – 12132 = 0

∴ n ^{2} + 337 n – 36 n – 12132 = 0

∴ n (n + 337) – 36 (n + 337) = 0

∴ (n + 337) (n – 36) = 0

∴ n = 36 and n = – 337

Here, we reject n = – 337 because months value can not be negative, hence n = 36

hence, time period, n = 36 months = 3 years

**Therefore, time period of RD account is 36 months or 3 years.**

*Check: For time period of 36 months, money invested is 400 x 36 = 14400*

*Interest Amount, I = P × *

*= 400 x *

*= 400 x 18 x 37 x *

*= 4 x 6 x 37 x 2 = 1776*

*Total maturity amount = 14400 + 1776 = 16176*

*Since it matches the given maturity amount in question, hence our answer is correct.*

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