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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.
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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 × 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.
RELATED QUESTIONS
A page from a savings bank account passbook is given below:
| Date | Particulars | Amount withdrawn (Rs.) |
Amount Deposited (Rs.) |
Balance (Rs.) |
| Jan 7, 2016 | B/F | 3,000.00 | ||
| Jan 10, 2016 | By Cheque | 2600.00 | 5600.00 | |
| Feb 8, 2016 | To Self | 1500.00 | 4100.00 | |
| Apr 6, 2016 | By Cheque | 2100.00 | 2000.00 | |
| May 4, 2016 | By Cash | 6500.00 | 8500.00 | |
| May 27, 2016 | By Cheque | 1500.00 | 10000.00 |
1) Calculate the interest for the 6 months from January to June 2016, at 6% per annum.
2) If the account is closed on 1st July 2016, find the amount received by the account holder.
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