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प्रश्न
Suresh has a recurring deposit account in a bank. He deposits ₹ 2000 per month and the bank pays interest at the rate of 8% per annum. If he gets ₹ 1040 as interest at the time of maturity, find in years total time for which the account was held.
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उत्तर
Deposit per month P = ₹ 2000
Rate of interest R = 8%
Interest earned, I = ₹ 1040
Let n months be the length of time for which money is invested.
Then, by formula
I = `(P xx n(n + 1))/(2 xx 12) xx r/100`
1040 = `2000 xx (n(n + 1))/(2 xx 12) xx 8/100`
1040 = `(20 xx n xx (n + 1))/3`
52 × 3 = n2 + n
n2 + n – 156 = 0
n2 + 13n – 12n – 156 = 0
n(n + 13) – 12(n + 13) = 0
(n – 12)(n + 13) = 0
n = 12 ...(∵ n = –13, is not possible)
As a result, the time period for which money is invested is 12 months or 1 year.
संबंधित प्रश्न
Ritu has a Recurring Deposit Account in a bank and deposits Rs. 80 per month for 18 months. Find the rate of interest paid by the bank if the maturity value of the account is Rs. 1,554.
Deepa has a 4-year recurring deposit account in a bank and deposits Rs 1,800 per month. If she gets Rs 1,08,450 at the time of maturity, find the rate of interest.
Mrs. Goswami deposits Rs. 1000 every month in a recurring deposit account for 3 years at 8% interest per annum. Find the matured value.
Mr. S.K. Mishra had a Savings Bank Account in Punjab National Bank. His Passbook had the following entries:
| Date | Particulars | Withdrawals (in ₹) |
Deposits (in ₹) |
Balance (in ₹) |
| 1998, Jan. 8 | By Cash | - | 500·00 | 500·00 |
| March 19 | To Cheque No. 626 | 100·00 | - | 400·00 |
| May 23 | By Cheque | - | 1500·00 | 1,900·00 |
| July 29 | To Withdrawals Slip | 200·00 | - | 1,700·00 |
| Sept 2 | By Cash | - | 1,300·00 | 3,000·00 |
If the interest is paid at the rate of 5% per annum at the end of September every year, calculate the amount he will get if he closes the account on October 30, of the same year.
The entries in the passbook of a Saving Bank Account holder are as follows:
| Date | Particulars | Withdrawals(₹) | Deposits(₹) | Balance(₹) |
| Feb. 12, 1986 | By cash | - | 2,000·00 | 2,000·00 |
| March 10 | By cash | - | 1,100·00 | 3,100·00 |
| April 20 | To cheque no. 231 | 800·00 | - | 2,300·00 |
| April 25 | By cash | - | 700·00 | 3,000·00 |
| May 11 | To cheque no. 232 | 700·00 | - | 2,300·00 |
| July 2 | By cash | - | 400·00 | 2,700·00 |
| July 8 | By cash | - | 500·00 | 3,200·00 |
| Aug. 10 | By cash | - | 600·00 | 3,800·00 |
| Aug. 28 | To cheque no. 233 | 200·00 | - | 3,600·00 |
Rate of interest is 5% per annum. Calculate the interest due if the account is closed on:
(i) September 29, 1986
(ii) October 1, 1986.
Mr. Ashok has an account in the Central Bank of India. The following entries are from his passbook:
| Date | Particulars | Withdrawals (₹) |
Deposits (₹) |
Balance (₹) |
| 01-01-05 | B/F | - | - | 1,200·00 |
| 07-01-05 | By cash | 500·00 | 1,700·00 | |
| 17-01-05 | To cheque | 400·00 | - | 1,300·00 |
| 10-02-05 | By cash | - | 800·00 | 2,100·00 |
| 25-09-05 | By cheque | 500·00 | - | 1,600·00 |
| 20-09-05 | By cash | - | 700·00 | 2,300·00 |
| 21-11-05 | To cheque | 600·00 | - | 1,700·00 |
| 05-12-05 | By cash | - | 300·00 | 2,000·00 |
If Mr. Ashok gets Rs. 83.75 as interest at the end of the year where the interest is compounded annually, calculate the rate of interest paid by the bank in his Savings Bank Account on 31st December 2005.
A page from the saving bank account of Priyanka is given below:
| Date | Particulars | Amount withdrawn(₹) |
Amount deposited (₹) |
Balance (₹) |
| 3/4/2006 | B/F | - | - | 4,000·00 |
| 5/4/2006 | By Cash | - | 2,000·00 | 6,000·00 |
| 18/4/2006 | By cheque | - | 6,000·00 | 12,000·00 |
| 25/5/2006 | To cheque | 5,000·00 | - | 7,000·00 |
| 30/5/2006 | By cash | - | 3,000·00 | 10,000·00 |
| 20/7/2006 | By self | 4,000·00 | - | 6,000·00 |
| 10/9/2006 | By cash | - | 2,000·00 | 8,000·00 |
| 19/9/2006 | To cheque | 1,000·00 | - | 7,000·00 |
If the interest earned by Priyanka for the period ending September 2006 is Rs. 175, find the rate of interest.
₹ 900 is deposited every month in a recurring deposit account at 10% rate of interest, the interest earned in 8 months is ______.
A man gets ₹ 1,404 as interest at the end of one year. If the rate of interest is 12% per annum in R.D. account, the monthly instalment is ______.
Manish opened an R.D. account in a bank and deposited ₹ 1,000 per month at the interest of 10% per annum and for 2 years. The total money deposited by him is ______.
