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प्रश्न
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.
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उत्तर
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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संबंधित प्रश्न
Virat opened a Savings Bank account in a bank on 16th April 2010. His pass book shows the following entries:
| Date | Particulars |
Withdrawal (Rs.) |
Deposit (Rs.) | Balance (Rs.) |
| April 16, 2010 | , By cash | - | 2500 | 2500 |
| April 28th | By cheque | - | 3000 | 5500 |
| May 9th | To cheque | 850 | - | 4650 |
| May 15th | By cash | 1600 | 6250 | |
| May 24th | To cash | 1000 | - | 5250 |
| June 4th | To cash | 500 | - | 4750 |
| June 30th | To cheque | - | 2400 | 7150 |
| July 3rd | By cash | - | 1800 | 8950 |
Calculate the interest Virat earned at the end of 31st July 2010 at 4% per annum interest. What sum of money will he receive if he closed the account on 1st August 2010?
A page from the Savings Bank Account of Mr Prateek is given below:
| Date | Particulars | Withdrawal (In Rs.) |
Deposit (In Rs.) |
Balances (In Rs.) |
| January 1st, 2006 | B/F | - | - | 1270 |
| January 7th, 2006 | By Cheque | - | 2310 | 3580 |
| March 9th, 2006 | To Self | 2000 | - | 1580 |
| June 26th, 2006 | By Cash | - | 6200 | 7780 |
| June 10th 2006 | To Cheque | 4500 | - | 3280 |
| July 15th, 2006 | By Clearing | - | 2630 | 5910 |
| October 18th, 2006 | To Cheque | 530 | - | 5380 |
| October 27th, 2006 | To Self | 2690 | - | 2690 |
| November 3rd, 2006 | By Cash | - | 1500 | 4190 |
| December 6th, 2006 | To Cheque | 950 | - | 3240 |
| December 23rd, 2006 | By Transfer | - | 2920 | 6260 |
If he receives Rs. 198 as interest on 1st January 2007, find the rate of interest paid by the bank.
Mr. Gupta opened a recurring deposit account in a bank. He deposited Rs. 2500 per month for two years. At the time of maturity he got Rs. 67,500. Find:
1) the total interest earned by Mr Gupta.
2) the rate of interest per annum.
Mrs. Geeta deposited Rs. 350 per month in a bank for 1 year and 3 months under the Recurring Deposit Scheme. If the maturity value of her deposits is Rs. 5,565; find the rate of interest per annum.
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Shrikant deposited 85,000 rupees for `2 1/2` years at 7 p.c.p.a. in a savings bank account. What is the total interest he received at the end of the period?
At a certain rate of interest, the interest after 4 years on 5000 rupees principal is 1200 rupees. What would be the interest of 15000 rupees at the same rate of interest for the same period?
Lataben borrowed some money from a bank at a rate of 10 p.c.p.a. interest for `2 1/2` years to start a cottage industry. If she paid 10250 rupees as total interest, how much money had she borrowed?
Fill in the blanks in the table.
| Principal | Rate of interest (p.c.p.a.) | Time | Interest | Amount |
| 4200 | 7% | 3 years | ...... | ...... |
Fill in the blanks in the table.
| Principal | Rate of interest (p.c.p.a.) | Time | Interest | Amount |
| 8000 | 5% | ...... | 800 | ...... |
