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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
Given below are the entries in a Saving Bank A/c passbook.
| Date | Particulars | Withdrawals | Deposit | Balance |
| Feb8 | B/F | - | - | Rs. 8500 |
| Feb 18 | To self | Rs. 4000 | - | |
| April 12 | By cash | - | Rs. 2230 | |
| June 15 | To self | Rs. 5000 | - | |
| July 8 | By cash | - | Rs. 6000 |
Calculate the interest for six months from February to July at 6% p.a.
Mr. Bajaj needs Rs. 30,000 after 2 years. What least money (in multiple of 5) must he deposit every month in a recurring deposit account to get required money at the end of 2 years, the rate of interest being 8% p.a.?
A page from the passbook of Mr. Rohit is given below. The interest accrued for the period January to December 2006 at a certain rate of interest per annum is Rs. 377.40. without taking the principal as the nearest multiple of Rs. 10, calculate the rate:
| Date | Particulars | Debit (Rs) | Credit (Rs) | Balance (Rs) |
| 2006 | ||||
| Jan 1 | Balance B/F | 7,500.00 | ||
| March 7 | By Cheque | 1,875.00 | ||
| March 10 | By Cash | 625.00 | ||
| July 17 | To self | 3,250.00 | ||
| Oct 5 | By Cheque | 2,160.00 | ||
| Dec 19 | To Cheque | 1,340.00 |
Given below is a page from the passbook of the savings bank account of Mr. Rajesh. Complete the entries in the passbook and calculate the interest paid to him by the bank at 6°/o pa in the end of June.
| Date | Particulars | Withdrawals | Deposits | Balance |
| 08.02.2008 | By Cash | 12000.00 | ||
| 15.03.2008 | To cash | 3000.00 | ||
| 08.04.2008 | To Cheque | 2500.00 | ||
| 18.04.2008 | By Cash | 16000.00 | ||
| 10.06.2008 | By Cash | 800.00 |
Mr. Richard has a recurring deposit account in a post office for 3 years at 7.5% p.a. simple interest. If he gets Rs. 8,325 as interest at the time of maturity, find:
- the monthly instalment.
- the amount of maturity.
Sharukh opened a recurring deposit account in a bank and deposited Rs 800 per month for `1 1/2` years. If he recieved Rs 15,084 at the time of maturity, find the rate of interest per annum.
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.
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.
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.
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 ______.
