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| Date | Transaction | Amount |
|---|---|---|
| 01 Mar 2013 | Deposit | 1200 |
| 02 Mar 2013 | Withdrawal | 100 |
| 10 Mar 2013 | Withdrawal | 400 |
| 15 Mar 2013 | Deposit | 200 |
| 16 Mar 2013 | Withdrawal | 900 |
| 18 Mar 2012 | Deposit | 200 |
| 21 Mar 2012 | Deposit | 700 |
| 31st Mar 2013 | Withdrawal | 100 |
Daily Compounding - Monthly Posting Using Daily Balance Method
The account activity breaks down into the following End of Day Balances:
Monthly Posting so we want to post interest to the account for periods (01 Mar - 31 Mar), (01 Apr - 30 Apr), (01 May - 31 May), (01 Jun - 30 Jun)
Compound Interest Forumula using in Daily Compounding:
The future value of a savings account balance on a given end of day is calculated using the following:
| Panel | ||
|---|---|---|
| ||
FV = PV x (1 + r)^n where, PV = The end of day balance e.g. 1200 r = periodic interest rate so in this case daily interest rate which is worked out by dividing 1 by 365 (number of days in year) and mulitplying by 0.05 (5%) n = number of compounding periods the balance/PV will compound - in the same period as the periodic interest rate - so in this case Days. So if a balance exists for 5 days we use n=5 to calculate what the balance produces in interest when compounding. |
Summary:
- Interest earned for march period is 3.404739630 - 3.40 will over the four months results in interest of 13.48 will be posted to clients account mean the client loses out by 0.004739630 in this posting period. It results in client having a Loss of 0.003506984 due to rounding of interest earned at posting.
| Date | Up to & (inclusive) | Days | Type | Amount | Opening Bal | Closing Bal | Interest on Bal | Interest To Date | Bal for Compounding | (I) Posted | Gain/Loss Due To Rounding |
|---|---|---|---|---|---|---|---|---|---|---|---|
01/03/2013 | 01/03/2013 | 1 | Deposit | 1200 | 0 | 1200 | 0.164383562 | 0.164383562 | 1200.164383562 | ||
| 02/03/2013 | 09/03/2013 | 8 | Withdrawal | 100 | 1200 | 1100 | 1.206237813 | 1.370621375 | 1,101.370621375 | ||
| 10/03/2013 | 14/03/2013 | 5 | Withdrawal | 400 | 1100 | 700 | 0.480522469 | 1.851143844 | 701.851143844 | ||
| 15/03/2013 | 15/03/2013 | 1 | Deposit | 200 | 700 | 900 | 0.123541253 | 1.974685097 | 901.974685097 | ||
| 16/03/2013 | 17/03/2013 | 2 | Withdrawal | 900 | 900 | 0 | 0.000541047 | 1.975226144 | 1.975226144 | ||
| 18/03/2013 | 20/03/2013 | 3 | Deposit | 200 | 0 | 200 | 0.083014888 | 2.058241032 | 202.058241032 | ||
| 21/03/2013 | 30/03/2013 | 10 | Deposit | 700 | 200 | 900 | 1.236458229 | 3.294699261 | 903.294699261 | ||
| 31/03/2013 | 31/03/2013 | 1 | Withdrawal | 100 | 900 | 800 | 0.110040370 | 3.404739631 | 803.404739631 | 3.40 | -0.004739631 |
| 01/04/13 | 30/04/2013 | 30 | Interest Posting | 3.40 | 800 | 803.40 | 3.308210288 | 3.308210288 | 806.708210288 | 3.31 | +0.001789712 |
| 01/05/13 | 31/05/2013 | 31 | Interest Posting | 3.31 | 803.40 | 806.71 | 3.432803347 | 3.432803347 | 810.142803347 | 3.43 | -0.002803347 |
| 01/06/13 | 30/06/2013 | 30 | Interest Posting | 3.43 | 806.71 | 810.14 | 3.335964006 | 3.335964006 | 813.475964006 | 3.34 | +0.004035994 |
| 122 | 813.48 | 13.48 |
| Transaction | Date | Amount | Balance(EOD) | Number of Days | Cumulative Balance |
|---|---|---|---|---|---|
| Balance | 28th Feb 2013 | 0 | 0 | - | 0 |
| Deposit | 1st Mar 2013 | 1200 | 1200 | 1 | 1200 |
| Withdrawal | 2nd Mar 2013 | 100 | 1100 | 8 | 8800 |
| Withdrawal | 10th Mar 2013 | 400 | 700 | 5 | 3500 |
| Deposit | 15th Mar 2013 | 200 | 900 | 1 | 900 |
| Withdrawal | 16th Mar 2013 | 900 | 0 | 2 | 0 |
| Deposit | 18th Mar 2013 | 200 | 200 | 3 | 600 |
| Deposit | 21st Mar 2013 | 700 | 900 | 10 | 7000 |
| Withdrawal | 31st Mar 2013 | 100 | 800 | 1 | 800 |
| 31 Days | 22800 |
Compounded Daily on Daily Balance
Based on 365 days in year, Nominal Annual Interest Rate: 5% and a daily compounding period, monthly crediting period:
Daily Rate is: 0.0001369863014 ==> (0.05 x (1/365)).
The formula is: Interest = Balance x Daily Rate (DR) x Number of Days
The Balance in this case is always the end of day blance plus and cumulative interest earned in the compounding periods before hand (which in this case is previous days).
| Date | Starting Bal | End Of Period Bal | Days | Interest Earned | Total Interest Compounded |
|---|---|---|---|---|---|
| 1st Mar | 0 | 1200 | 1 | 1200 x 0.0001369863014 = 0.1643835617 | 0.164383562 |
| 2nd Mar | 1200 | 1100 | 1 | 1100 + (compounded interest to date) x DR = 0.1507074499 | 0.3150910116 |
| 3rd Mar | 1100 | 1100 | 1 | 1100 + (compounded interest to date) x DR = 0.1507280947 | 0.4658191063 |
| 1100 | 1100 | 1 | 1100 + (compounded interest to date) x DR = 0.1507487424 | 0.6165678487 | |
| 1100 | 1100 | 1 | 1100 + (compounded interest to date) x DR = 0.1507693929 | 0.7673372416 | |
| 1100 | 1100 | 1 | 1100 + (compounded interest to date) x DR = 0.1507900462 | 0.9181272878 | |
| 1100 | 1100 | 1 | 1100 + (compounded interest to date) x DR = 0.1508107024 | 1.068937990 | |
| 1100 | 1100 | 1 | 1100 + (compounded interest to date) x DR = 0.1508313614 | 1.219769351 | |
| 9th Mar | 1100 | 1100 | 1 | 1100 + (compounded interest to date) x DR = 0.1508520232 | 1.370621374 |
| 10th Mar | 1100 | 700 | 1 | 700 + (compounded interest to date) x DR = 0.09607816734 | 1.466699541 |
| 700 | 700 | 1 | 700 + (compounded interest to date) x DR = 0.09609132872 | 1.562790870 | |
| 700 | 700 | 1 | 700 + (compounded interest to date) x DR = 0.09610449193 | 1.658895362 | |
| 13th Mar | 700 | 700 | 1 | 700 + (compounded interest to date) x DR = 0.09611765693 | 1.755013019 |
| 14th Mar | 700 | 700 | 1 | 700 + (compounded interest to date) x DR = 0.09613082372 | 1.851143843 |
| 15th Mar | 700 | 900 | 1 | 900 + (compounded interest to date) x DR = 0.1235412526 | 1.974685096 |
| 16th Mar | 900 | 0 | 1 | 0 + (compounded interest to date) x DR = 0 | 1.974685096 |
| 17th Mar | 0 | 0 | 1 | 0 | 1.974685096 |
| 18th Mar | 0 | 200 | 1 | 200 + (compounded interest to date) x DR = 0.02766776509 | 2.002352861 |
| 19th Mar | 200 | 200 | 1 | 200 + (compounded interest to date) x DR = 0.02767155520 | 2.030024416 |
| 20th Mar | 200 | 200 | 1 | 200 + (compounded interest to date) x DR = 0.02767534581 | 2.057699762 |
| 21st Mar | 200 | 900 | 1 | 900 + (compounded interest to date) x DR = 0.1235695479 | 2.181269310 |
| 900 | 900 | 1 | 900 + (compounded interest to date) x DR = 0.1235864753 | 2.304855785 | |
| 900 | 900 | 1 | 900 + (compounded interest to date) x DR = 0.1236034049 | 2.428459190 | |
| 900 | 900 | 1 | 900 + (compounded interest to date) x DR = 0.1236203369 | 2.552079527 | |
| 900 | 900 | 1 | 900 + (compounded interest to date) x DR = 0.1236372712 | 2.675716798 | |
| 900 | 900 | 1 | 900 + (compounded interest to date) x DR = 0.1236542078 | 2.799371006 | |
| 900 | 900 | 1 | 900 + (compounded interest to date) x DR = 0.1236711467 | 2.923042153 | |
| 900 | 900 | 1 | 900 + (compounded interest to date) x DR = 0.1236880880 | 3.046730241 | |
| 900 | 900 | 1 | 900 + (compounded interest to date) x DR = 0.1237050316 | 3.170435273 | |
| 900 | 900 | 1 | 900 + (compounded interest to date) x DR = 0.1237219775 | 3.294157250 | |
| Mar 31st | 900 | 800 | 1 | 800 + (compounded interest to date) x DR = 0.1100402955 | 3.404197546 |
| 800 | 31 | Total interest earned = 3.40 credited on 1st April 2013 | =3.404197546Loss of 0.003506984 |
Compounded Monthly on Daily Balance
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| Transaction | Date | Amount | Balance(EOD) | Number of Days | Cumulative Balance |
|---|---|---|---|---|---|
| Account Activated | 26th Jan 2012 | 0 | 0 | - | 0 |
| Deposit | 26th Jan 2012 | 100,000 | 100,000 | 1 | 100,000 |
| Withdrawal | 27th Jan 2012 | 100,000 | 0 | 5 | 0 |
| 6 Days | 100,000 |
Compounded Daily on Daily Balance
Nominal Annual Interest Rate: 12% (r=0.12)
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