Question

Rajiv Bhardwaj has a recurring deposit account in a bank of Rs 600 per month. If the bank pays simple interest of 7% p.a. and he gets Rs 15450 as maturity amount, find the total time for which the account was held.

Answer 1

Deposit during the month (P) = Rs 600

Rate of interest = 7% p.a.

Amount of maturity = Rs 15450

Let time = n months

∴ Total principal

= `("P"("n")("n" + 1))/(2)`

= `(600 xx "n"("n" + 1))/(2)`

= `(600("n"^2 + "n"))/(2)`

= 300(n² + n)

∴ Interest

= `"PRT"/(100)`

= `(300("n"^2 + "n") xx 7 xx 1)/(100 xx 12)`

= `(7)/(4)("n"^2 + "n")`

∴ `600"n" + (7)/(4)("n"^2 + "n")` = 15450

⇒ 2400n + 7n² + 7n = 61800

⇒ 7n² + 2407n - 61800 = 0

⇒ 7n² - 168n + 2575n - 61800 = 0

⇒ 7n(n - 24) + 2575(n - 24) = 0

⇒ (n - 24) (7n + 2575) = 0

Either n - 24 = 0, then n = 24

or

7n + 2575 = 0, then

7n = -2575

⇒ n = `(-2575)/(7)`

Which is not possible being negative.

∴ n = 24

∴ Period = 24 months or 2 years.