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प्रश्न
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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उत्तर
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.
संबंधित प्रश्न
Rishabh has the recurring deposit account in a post office for 3 years at 8% p.a. simple interest. If he gets Rs 9,990 as interest at the time of maturity, find:
1) The monthly instalment.
2) The amount of maturity.
A page from a passbook of savings bank account is given below:
| Date | Particulars | Amount Withdrawn (In Rs) |
Amount Deposits (In Rs) |
Balance (In Rs) |
| 09.08.1999 11.08.1999 05.10.1999 10.10.1999 27.11.1999 29.11.1999 |
By Cash By Cheque To Cheque By Cash By Cheque By Cash |
- - 12,000 - 5,000 - |
10,000 5,000 - 17,000 - 3,000 |
10,000 15,000 3,000 20,000 15,000 18,000 |
The account is closed on 2nd Jan, 2000. Find the amount received, if the rate of interest is 5%
A page from the passbook of Asha is given below:
| Date | Particulars | Amount Withdrawn (Dr) Rs P | Amount Deposits (Cr) Rs. P | Balance Rs. P |
| Jan 5 March 7 April 2 April 10 Oct , 6 Dec, 8 |
Balance B/F To Cheque By Cheque By Cheque By Cheque By Cash |
1,200.00
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2,300.00
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|
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|
Complete the passbook and then calculate the interest for the period January to December 5% per annum.
Mr. Banerjee opens a recurring deposit account for Rs 3,000 per month at 9% simple interest pa. On maturity, he gets Rs. 1,70,460. Find the period for which he continued with the account.
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Amount Deposited (in ₹) |
Balance (in ₹) |
| Jan. 1 | By Balance | - | - | 2,100·00 |
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| Feb. 15 | To Cheque | 2,000·00 | - | 1,600·00 |
| March 15 | By Cash | - | 2,000·00 | 3,600·00 |
| March 20 | To Cheque | 1,000·00 | - | 2,600·00 |
| June 12 | By Cash | - | 3,000·00 | 5,600·00 |
| June 28 | To Cheque | 1,000·00 | - | 4,600·00 |
| Oct. 15 | To Cheque | 3,000·00 | - | 4,600·00 |
| Nov. 5 | By Cash | - | 1,500·00 | 3,100·00 |
| Dec. 10 | By Cash | - | 500·00 | 3,600·00 |
| Dec. 20 | To Cheque | 1,000·00 | - | 2,600·00 |
If the rate of interest decreases from 5% to 4% with effect from June 1st, 2002, compute the interest at the end of the year.
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Amount Deposits(₹) | Amount Balance(₹) |
| Jan. 4, 2007 | By Cash | - | 1,000·00 | 1,000·00 |
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| Feb. 3, 2007 | By Cash | - | 2,500·00 | 6,500·00 |
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| May 25, 2007 | By Cash | - | 2,000·00 | 11,500·000 |
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