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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
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?
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. Mathew opened a Recurring Deposit Account in a certain bank and deposited ₹ 640 per month for 4 ½ years. Find the maturity value of this account, if the bank pays interest at the rate of 12% per year.
Each of A and B both opened a recurring deposit accounts in a bank. If A deposited Rs. 1,200 per month for 3 years and B deposited Rs. 1,500 per month for 2 ½ years; find, on maturity, who will get more amount and by how much? The rate of interest paid by the bank is 10% per annum.
A man has a Recurring Deposit Account in a bank for `3 1/2` years. If the rate of interest is 12% per annum and the man gets Rs. 10,206 on maturity, find the value of monthly instalments.
Mr. Gulati has a Recurring Deposit Account of Rs. 300 per month. If the rate of interest is 12% and the maturity value of this account is Rs. 8,100; find the time (in years) of this Recurring Deposit Account.
Ms. Chitra opened a saving bank account with SBI on 05.04.2007 with a cheque deposit of Rs 11,000/.Subsequently, she took out Rs 3,200/- on 12.05.2007; deposited a cheque of Rs. 8,800/- on 03.06.2007 and paid Rs 2,000/- by cheque on 18.06.2007.
If the rate of simple interest was 5% pa compounded at the end of March and September, find her balance on 1.04.2008
If Rihanna deposits 1500 rupees in the school fund at 9 p.c.p.a for 2 years, what is the total amount she will get?
Javed deposited 12000 rupees at 9 p.c.p.a. in a bank for some years, and withdrew his interest every year. At the end of the period, he had received altogether 17,400 rupees. For how many years had he deposited his money?
Fill in the blanks in the table.
| Principal | Rate of interest (p.c.p.a.) | Time | Interest | Amount |
| ...... | 6% | 4 years | 1200 | ...... |
