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Question
A recurring deposit account of Rs. 1,200 per month has a maturity value of Rs. 12,440. If the rate of interest is 8% and the interest is calculated at the end of every month; find the time (in months) of this Recurring Deposit Account.
Solution
Installment per month (P) = Rs. 1,200
Number of months (n) = n
Let rate of interest (r) = 8% p.a.
∴ `S.I. = P xx (n(n +1))/(2 xx 12) xx r/100`
= `1200 xx (n(n + 1))/(2 xx 12) xx 8/100`
= `1200 xx (n(n + 1))/24 xx 8/100`
= Rs. 4n(n + 1)
Maturity value = Rs. (1,200 × n) + Rs. 4n(n + 1)
= Rs. (1200n + 4n2 + 4n)
Given maturity value = Rs. 12,440
Then 1200n + 4n2 + 4n = 12,440
⇒ 4n2 + 1204n – 12440 = 0
⇒ n2 + 301n – 3110 = 0
⇒ (n + 311)(n – 10) = 0
⇒ n = – 311 or n = 10 months
Then number of months = 10
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