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Question
Ankita started paying Rs 400 per month in a 3 years recurring deposit. After six months her brother Anshul started paying Rs 500 per month in a `2(1)/(2)` years recurring deposit. The bank paid 10% p.a. simple interest for both. At maturity who will get more money and by how much?
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Solution
In case of Ankita,
Deposit per month = Rs 400
Period (n) = 3 years = 36 months
Rate of interest = 10%
Total principal for one month
= `400 xx ("n"("n" + 1))/(2)`
= `400 xx (36(36 + 1))/(2)`
= `₹(400 xx 36 xx 37)/(2)`
= ₹ 266400
Interest
= `"prt"/(100)`
= `(266400 xx 10 xx 1)/(100 xx 12)`
= ₹ 2220
∴ Amount of maturity
= ₹ 400 × 36 + ₹ 2220
= ₹ 14400 + ₹ 2220
= ₹ 16620
In case of Anshul,
Deposit P.m. = ₹ 500
Rate of interest = 10%
Period (n) = `2(1)/(2)` year = 30months
∴ Total principal for one month
= `₹500 xx ("n"("n" + 1))/(2)`
= `500 xx (30(30 + 1))/(2)`
= `₹(500 xx 30 xx 31)/(2)`
= ₹ 232500
Interest
= `(232500 xx 10 xx 1)/(100 xx 12)`
= ₹ 1937.50
Amount of maturity
= ₹ 500 × 30 + ₹ 1937.50
= ₹ 15000 + ₹ 1937.50
= ₹ 16937.50
At maturity Anshul will get more amount
DIfference
= ₹ 16937.50 - ₹ 16620.00
= ₹ 317.50.
RELATED QUESTIONS
A page from a savings bank account passbook is given below:
| Date | Particulars | Amount withdrawn (Rs.) |
Amount Deposited (Rs.) |
Balance (Rs.) |
| Jan 7, 2016 | B/F | 3,000.00 | ||
| Jan 10, 2016 | By Cheque | 2600.00 | 5600.00 | |
| Feb 8, 2016 | To Self | 1500.00 | 4100.00 | |
| Apr 6, 2016 | By Cheque | 2100.00 | 2000.00 | |
| May 4, 2016 | By Cash | 6500.00 | 8500.00 | |
| May 27, 2016 | By Cheque | 1500.00 | 10000.00 |
1) Calculate the interest for the 6 months from January to June 2016, at 6% per annum.
2) If the account is closed on 1st July 2016, find the amount received by the account holder.
A page from the passbook of a savings book account in a particular year is given below:
| Date | Particulars | Debit (In Rs) | Credit (In Rs) | Balance (In Rs) |
| Jan 3 | By cash | 5,000.00 | 5,000.00 | |
| Feb 13 | To self | 500.00 | ||
| March 24 | By cheque | 2,000.00 | ||
| March 31 | By Interest | |||
| May 20 | By cash | 800.00 | ||
| July 7 | To Cheque | 1,400.00 | ||
| July 18 | By cash | 1,600.00 | ||
| Sept 15 | To Cheque | 3,200.00 | ||
| Sept 26 | By Cheque | 2,350.00 |
If the interest is calculated at 6% P.a. and is compounded at the end of march and September at every year, find the interest earned up to 31st march and then after completing all the entries, find the amount that the account holder would have received had he closed the account on 20th October the same year.
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 |
Mrs. N. Batra has a savings bank account with the Punjab National bank. She had the following transactions (from 1st January, 2007 to 31st December, 2007) with the bank:
(i) 01-01-2007; B/F Rs. 8,764/-
(ii) 13-03-2007; deposited Rs. 6,482
(iii) 22-06-2007; withdrew Rs. 4,369
(iv) 09-08-2007; withdrew Rs. 1,333
(v) 24-11-2007; Deposited Rs. 2,158
Calculate the interest the accrured upto 31st December, 2007: if the rate of interest is 5% compounded yearly and the principle for every month is taken as the nearest multiple of Rs.10.
Taking the rate of interest as 6% per annum, find the amount that Mr. verma gets on closing the account.
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 |
The following are the entries in the passbook of a saving account of Ananya during the year 2007. If interest is calculated at 5 % pa, find the interest earned by Ananya during the year
| Date | Particulars | Withdrawals | Deposits | Balance |
| 01.01.2007 | By B/F | 6500.00 | ||
| 05.02.2007 | By Cheque | 7500.00 | 14000.00 | |
| 09.02.2007 | To Cash | 1500.00 | 12500.00 | |
| 06.06.2007 | By Cash | 1725.00 | 14225.00 | |
| 08.09.2007 | By Cheque | 375.00 | 14600.00 | |
| 06.11.2007 | By Cash | 6000.00 | 20600.00 | |
| 10.12.2007 | To Cheque | 2500.00 | 18100.00 |
The following enb·ies are from the saving bank account passbook of Mr. Ratnesh. If the rate of interest paid by the bank is 4. 5°/op.a. calculated at the end of March and September, find the balance in his account at the end of the year.
| Date | Particulars | Withdrawls | Deposits | Balance |
| 03.01.2006 | By B/F | 17900.00 | ||
| 09.01.2006 | To Cash | 3700.00 | 14200.00 | |
| 06.02.2006 | To Cheque | 2450.00 | 11750.00 | |
| 21.02.2006 | By Cash | 15600.00 | 27350.00 | |
| 17.03.2006 | By Cash | 9850.00 | 37200.00 | |
| 31.03.2006 | By Interest | |||
| 06.06.2006 | To Cheque | 4100.00 | ||
| 22.08.2006 | To Cash | 1500.00 | ||
| 05.09.2006 | By Cheque | 17300.00 | ||
| 09.09.2006 | To Cash | 6300.00 | ||
| 30.09.2006 | By Interest | |||
| 04.12.2006 | To Cash | 3000.00 | ||
| 11.12.2006 | By Cheque | 11760.00 |
A page from the Savings Bank Account of Mr. Prateek is given below:
| Date | Particulars | Withdrawals (in ₹) |
Deposits (in ₹) |
Balance (in ₹) |
| January 1st, 2006 | B/F | - | - | 1,270 |
| January 7th, 2006 | By Cheque | - | 2,310 | 3,580 |
| March 9th, 2006 | To Self | 2,000 | - | 1,580 |
| March 26th, 2006 | By Cash | - | 6,200 | 7,780 |
| June 10th, 2006 | To Cheque | 4,500 | - | 3,280 |
| July 15th, 2006 | By Clearing | - | 2,630 | 5,910 |
| October 18th, 2006 | To Cheque | 530 | - | 5,380 |
| October 27th, 2006 | To Self | 2,690 | - | 2,690 |
| November 3rd, 2006 | By Cash | - | 1,500 | 4,190 |
| December 6th, 2006 | To Cheque | 950 | - | 3,240 |
| December 23rd, 2006 | By Transfer | - | 2,920 | 6,160 |
If he receives ₹198 as interest on 1st January 2007, find the rate of interest paid by the bank.
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.
₹ 900 is deposited every month in a recurring deposit account at 10% rate of interest, the interest earned in 8 months is ______.
