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Question
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.
Solution
(i)
Balance on `3^"rd"` Jan. = Rs. 5,000
Balance on `13^"th" Feb. = Rs. 5,000 – Rs. 500 = Rs. 4,500
Balance on `24^"th"` Mar. = Rs. 4,500 + Rs. 2,000 = Rs. 6,500
Minimum balance for January = Rs. 5,000
Minimum balance for February = Rs. 4,500
Minimum balance for March = Rs. 4,500
Total principal = Rs. 14,000
Rate of interest = 6% p.a. and Time =`1/12`year
∴Interest = `(PxxRxxT)/100 = (14.000xx6xx1)/(100xx12) =Rs. 70 `
(ii)
Balance on `31^"st"` March = Rs. 6,500 + Rs. 70 = Rs. 6,570
Balance on `20^"th"` May = Rs. 6,570 + Rs. 800 = Rs. 7,370
Balance on `7^"th"` July = Rs. 7,370 – Rs. 1,400 = Rs. 5,970
Balance on `18^"th"` July = Rs. 5,970 + Rs. 1,600 = Rs. 7,570
Balance on `15^"th"` September = Rs. 7,065 – Rs. 3,200 = Rs. 4,370
Balance on `26^"th"` September = Rs. 4370 + Rs. 2,350 = Rs. 6,720
Minimum balance for April = Rs. 6,570
Minimum balance for May = Rs. 6,570
Minimum balance for June = Rs. 7,370
Minimum balance for July = Rs. 5,970
Minimum balance for August = Rs. 7,570
Minimum balance for September = Rs. 4,370
Total principal = Rs. 38,420
Rate = 6% and Time =`1/12` year
∴ Interest=` (PxxRxxT)/100 = (38,420xx6xx1)/(100xx12) = Rs. 192.10`
Balance on 1st October = Rs. 6,720 + Rs. 192.1 = Rs. 6,912.10
Since he closes his account on `20^"th"` October, then he will not receive any interest in this month. So he will get Rs. 6,912.10
