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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.
Solution
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 x 12
⇒ 240n + n2 + n = 831 x 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 = 36months or 3years.
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