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Question
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.
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Solution
Deposit per month = Rs 2000,
Rate of interest = 10%, Let period = n months
= `2000 xx ("n"("n" + 1))/(2)`
= 100n(n + 1) and interest
= `(1000"n"("n" + 1) xx 10 xx 1)/(100 xx 12)`
= `(100"n"("n" + 1))/(12)`
∴ Maturity value
= `2000 xx "n" + (100"n"("n" + 1))/(12)`
∴ `2000"n" + (100"n"("n" + 1))/(12)` = 83100
⇒ 24000n + 100n2 + 100m = 83100 × 12
⇒ 240n + n2 + n = 831 × 12
⇒ n2 + 241n − 9972 = 0
⇒ n2 + 277n − 36n − 9972 = 0
⇒ 2(n + 277) − 36(n + 277) = 0
⇒ (n + 277)(n − 36) = 0
Either n + 277 = 0, then n = −277, which is not possible.
or n −36 = 0, then x = 36
∴ Period = 36 months or 3 years.
RELATED QUESTIONS
Priyanka has a recurring deposit account of Rs. 1000 per month at 10% per annum. If she gets Rs. 5550 as interest at the time of maturity, find the total time for which the account was held.
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.
Rekha opened a recurring deposit account for 20 months. The rate of interest is 9% per annum and Rekha receives Rs. 441 as interest at the time of maturity. Find the amount Rekha deposited each month.
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. Dhoni has an account in the Union Bank of India. The following entries are from his passbook:
| Date | Particulars | Withdrawals (in ₹) |
Deposits (in ₹) |
Balance (in ₹) |
| Jan 3, 07 | B/F | - | - | 2,642·00 |
| Jan 16 | To self | 640.00 | - | 2,002·00 |
| March 5 | By cash | - | 850·00 | 2,852·00 |
| April 10 | To self | 1130.00 | - | 1,722·00 |
| April 10 | By cheque | - | 650·00 | 2372.00 |
| June 15 | By cash | 577.00 | - | 1,795·00 |
Calculate the interest from January 2007 to June 2007 at a rate of 4% per annum.
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.
Given the following details, calculate the simple interest at the rate of 6% per annum up to June, 30:
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| January 1 | - | 24,000·00 | 24,000·00 |
| January 20 | 5,000·00 | - | 19,000·00 |
| January 29 | - | 10,000·00 | 29,000·00 |
| March 15 | - | 8,000·00 | 37,000·00 |
| April 3 | - | 7,653·00 | 44,653·00 |
| May 6 | 3,040·00 | - | 41,613·00 |
| May 8 | - | 5,087·00 | 46,700·00 |
Haneef has a cumulative bank account and deposits Rs. 600 per month for a period of 4 years. If he gets Rs. 5880 as interest at the time of maturity, find the rate of interest.
Mr. Gupta opened a recurring deposit account in a bank. He deposited Rs. 2,500 per month for two years. At the time of maturity he got Rs. 67,500. Find:
- the total interest earned by Mr. Gupta.
- the rate of interest per annum.
Mrs. Asha Mehta deposit Rs 250 per month for one year in a bank’s recurring deposit account. If the rate of (simple) interest is 8% per annum, then the interest earned by her on this account is
