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प्रश्न
The maturity value of an R.D. Account is ₹ 16176. If the monthly instalment is ₹ 400 and the rate of interest is 8%; find the time (period) of this R.D Account.
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उत्तर
Installment per month (P) = Rs. 400
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`
= `400 xx (n(n + 1))/24 xx 8/100`
= Rs. `(4n(n + 1))/3`
Maturity value = Rs. (400 × n) + Rs. `(4n(n + 1))/3`
Given maturity value = Rs. 16,176
Then Rs. (400 × n) + Rs. `(4n(n + 1))/3` = Rs. 16,176
⇒ 1200n + 4n2 + 4n = Rs. 48,528
⇒ 4n2 + 1204n = Rs. 48,528
⇒ n2 + 301n – 12132 = 0
⇒ (n + 337)(n – 36) = 0
⇒ n = –337 or n = 36
Then number of months = 36 months
= 3 years
संबंधित प्रश्न
Mr Choudhury opened a Saving Bank Account at State Bank of India on 1st April 2007. The entries of one year as shown in his passbook are given below.
| Date | Particulars | Withdrawals (in Rs.) | Deposits (in Rs.) | Balance (in Rs.) |
| Ist April 2007 | By Cash | - | 8550.00 | 8550.00 |
| 12th- April 2007 | To Self | 1200.00 | -- | 7350.00 |
| 24th April 2007 | By Cash | - | 4550.00 | 11900.00 |
| 8th July 2007 | By Cheque | - | 1500.00 | 13400.00 |
| 10th Sept. 2007 | By Cheque | - | 3500.00 | 16900.00 |
| 17th Sept. 2007 | By Cheque | 2500.00 | - | 14400.00 |
| 11th Oct. 2007 | By Cash | - | 800.00 | 15200.00 |
| 6th Jan. 2008 | To Self | 2000.00 | - | 13200.00 |
| 9th March 2008 | By Cheque | - | 950.00 | 14150.00 |
If the bank pays interest at the rate of 5% per annum, find the interest paid on 1st April 2008. Give your answer correct to the nearest rupee.
Pramod deposits Rs. 600 per month in a Recurring Deposit Account for 4 years. If the rate of interest is 8% per year; calculate the maturity value of his account.
A savings bank account was opened by Mrs. Roy on 3.7.12 and closed on 31.01.13. The entries in the passbook of Mrs. Roy were as given below:
| Date | Particulars | Debit (In Rs) | Credit (In Rs) | Balance (In Rs) |
| 3.7.12 | By cash | 690.00 | ||
| 15.7.12 | By cash | 1,153.00 | ||
| 27.8.12 | By Cheque | 2,468.00 | ||
| 30.8.12 | To cash | 946.00 | ||
| 12.9.12 | To Cheque | 1,000.00 | ||
| 20.11.12 | By Cheque | 3,000.00 | ||
| 26.11.12 | By cash | 750.00 | ||
| 28.11.12 | To Cash | 1,570.00 |
(i) By finding the balance on different dates of entries calculate the interest earned by Mrs. Roy, For the period she had this savings bank account, at the rate of 6% p.a.
(ii) Also, calculate the interest when the principal for every month is taken as the nearest multiple of 10.
Given below are the entries in a Savings Bank A/c passbook:
| Date | Particulars | Withdrawals (in ₹) |
Deposits (in ₹) |
Balance (in ₹) |
| Feb 8 | B/F | - | - | ₹ 8,500 |
| Feb 18 | To self | ₹ 4,000 | - | - |
| April 12 | By cash | - | ₹ 2,230 | - |
| June 15 | To self | ₹ 5,000 | - | - |
| July 8 | By cash | - | ₹ 6,000 | - |
Calculate the interest for six months from February to July at 6 % p.a.
Suresh has joined a factory which pays wages by cheque only. He opens a S.B. account on Feb. 1, and his passbook has the following entries Upto 1st April of the year.
| Date | Particulars | Withdrawals(₹) | Deposits(₹) | Balance(₹) |
| Feb. 1 | By cash | - | 50·00 | 50·00 |
| Feb. 2 | By salary | - | 1,000·00 | 1,050·00 |
| Feb. 4 | To withdrawn slip | 200·00 | - | 850·00 |
| Feb. 15 | By overtime allowance | - | 300·00 | 1,150·00 |
| Feb. 24 | To Aslam | 100·00 | - | 1,050·00 |
| March 1 | By salary | - | 1,000·00 | 2,050·00 |
| March 7 | To cheque no. 212 | 500·00 | - | 1,550·00 |
| March 21 | To cheque no. 213 | 700·00 | - | 850·00 |
| March 27 | To self | 400·00 | - | 450·00 |
| Apr. 1 | By salary | - | 1,000·00 | 1,450·00 |
| Apr. 11 | By interest | - | - | - |
He closes the account on 11th April. Complete the entries for 11th April at the rate of 5%
Mrs. Goswami deposits Rs. 1000 every month in a recurring deposit account for 3 years at 8% interest per annum. Find the matured value. (2009)
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.
₹ 800 per month is deposited in an R.D. account for one and half years. If the depositor gets ₹ 2,280 as interest at the time of maturity, the rate of interest is ______.
₹ 50 per month is deposited for 20 months in a recurring deposit account. If the rate of interest is 10%; the maturity value is ______.
A certain money is deposited every month for 8 months in a recurring deposit account at 12% p.a. simple interest. If the interest at the time of maturity is ₹ 36, the monthly instalment is ______.
