Question

A recurring deposit account is opened with Dena Bank, Meerut Cantt. For this ₹ 2,000 per month (at 10% p.a.) is deposited in the bank. If the maturity value is ₹ 25,300, find the total time for which account was held.

Answer 1

Given,

P = ₹ 2,000

r = 10%

Maturity value = ₹ 25,300

Let 'n' be number of months for which the money is deposited.

By formula,

∴ I = `P xx (n(n + 1))/(2 xx 12) xx r/100`

Substituting values, we get:

⇒ I = `2,000 xx (n(n + 1))/(2 xx 12) xx 10/100`

= `2,000 xx (n(n + 1))/240`

= `(50n(n + 1))/6`

Total money deposited = ₹(2000 × n) = ₹2000n

∴ Maturity value = Total amount deposited + Interest

= `2,000 + (50n(n + 1))/6`

= `(12,000 + 50n(n + 1))/6`

= `(12,000 + 50n^2)/6`

Since, maturity value = ₹ 25,300

⇒ `(12050 + 50^2)/6 = 25,300`

⇒ 12050n + 50n² = 25300 × 6

⇒ 12050n + 50n² = 151800

⇒ 50n² + 12050n − 151800 = 0

⇒ 50(n² + 241n − 3036) = 0

⇒ n² + 241n − 3036 = 0

⇒ n² + 253n − 12n − 3036 = 0

⇒ n (n + 253) −12(n + 253) = 0

⇒ (n − 12) (n + 253) = 0

⇒ (n − 12) = 0 or (n + 253) = 0

⇒ n = 12 or n = −253

Time cannot be negative, so we take:

n = 12 months = 1 year

Hence, the RD account was held for 1 year.