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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.
Solution
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.
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