Question

Samita has a recurring deposit account in a bank of Rs 2000 per month at the rate of 10% p.a. If she gets Rs 83100 at the time of maturity. Find the total time for which the account was held.

Answer 1

Deposit per month = Rs 2000,
Rate of interest = 10%, Let period = n months

= `2000 xx ("n"("n" + 1))/(2)`

= 100n(n + 1) and interest

= `(1000"n"("n" + 1) xx 10 xx 1)/(100 xx 12)`

= `(100"n"("n" + 1))/(12)`

∴ Maturity value

= `2000 xx "n" + (100"n"("n" + 1))/(12)`

∴ `2000"n" + (100"n"("n" + 1))/(12)` = 83100

⇒ 24000n + 100n² + 100m = 83100 × 12

⇒ 240n + n² + n = 831 × 12

⇒ n² + 241n − 9972 = 0

⇒ n² + 277n − 36n − 9972 = 0

⇒ 2(n + 277) − 36(n + 277) = 0

⇒ (n + 277)(n − 36) = 0

Either n + 277 = 0, then n = −277, which is not possible.

or n −36 = 0, then x = 36

∴ Period = 36 months or 3 years.