Introduction
This page runs through interest calculation and compounding examples for Passbook style savings account.
There are two methods to calculate the interest on passbook savings:
- The daily balance method; and
- The average daily balance method.
The examples below use end-of-day-balances and refer to the interest posting & compounding periods used.
Terms
Compounding Period: is the span of time which at the end of the interest earned over this period on the savings account balance in accumulated with the balance of the account is applicable for interest calculations in future periods. As a result the interest is compounded. The following compounding period frequencies are supported:
- Daily: compounding occurs on the balance each day and is accumulated with the balance so that the next days interest calculation takes it into account.
- Monthly: compounding occurs on the interest earned over the entire month. Next months interest calculation is on the savings account blance + any interest earned in previous compounding period.
Posting Period: is the span of time which at the end of the interest earned over this period on savings account is credited or posted to the clients account. A posting period may include many compounding periods. The following posting period frequencies are supported:
- Monthly: The period mirrors the calendar month so periods are 01 Jan - 31 Jan, 01 Feb - 28 Feb, 01 Mar - 31 Mar etc
- Quarterly: The period mirrors the calendar quarter so periods are 01 Jan - 31 Mar, 01 Apr - 30 Jun etc
- Annually: Ther period mirrors the calendar year so perdios are 01 Jan - 31 Dec for each year.
Nominal annual interest rate %: Also known as nominal APR, its nominal as this rate doesnt reflect influences such as inflation or compounding. The percentage is represented as a number e.g. 20 for 20% NOT as a fraction 0.2 = 20%
Interest Calculation Method: We support Daily Balance and Average Daily Balance
Days in Year: Some people want their interest calculations to be done over a 360 day year instead of 365/366 day year.
Account Activity
The client makes the following transactions throughout the month on an account opened on 01 March 2013:
| 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
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)
Summary:
- Interest earned for march period is 3.404739630 - 3.40 will be posted to clients account mean the client loses out by 0.004739630 in this posting period
| 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 | =3.404197546 |
Compounded Monthly on Daily Balance
Based on 365 days in year, Nominal Annual Interest Rate: 5% and a monthly 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 months).
| Date | Starting Bal | End Of Period Bal | Days | Interest Earned | Total Interest Compounded |
|---|---|---|---|---|---|
| 1st Mar | 0 | 1200 | 1 | 0 | |
| 2nd Mar | 1200 | 1100 | 8 | 0 | |
| 10th Mar | 1100 | 700 | 5 | 0 | |
| 15th Mar | 700 | 900 | 1 | 0 | |
| 16th Mar | 900 | 0 | 2 | 0 | |
| 18th Mar | 0 | 200 | 3 | 0 | |
| 21st Mar | 200 | 900 | 10 | 0 | |
| 31st Mar | 900 | 800 | 1 | 0 | |
| 800 | 31 | Total interest earned = 3.40 credited on 1st April 2013 | =3.397260275 |
There is no difference between daily compounding and monthly compounding on what interest is credited at the end of the month after rounding: 3.40
The daily compounding results in (3.404197546 - 3.397260275 =) 0.006937271 more interest at the end of the month given the example account activity.
Compounding Monthly on Average Daily Balance
Average Balance Steps
The accumulated end-of-day balance of $24,800 is divided by the total number of days in the period (31) to find the average daily balance of $800.
The average daily balance should be rounded to five or more decimals, in this case $800.00000.
The periodic interest rate would be 0.00424657534 (0.5 x (1/365) x 31)
Step 1 5.0 divided by 100 Result: 0.05
Step 2 0.50 times 1/365 Result: 0.000136986
Step 3 0.000136986 times 31 Result: 0.004246575
Step 4 0.004246575 times $800 Result: 3.397260274
Step 5 Rounded Result: $3.40
MIFOSX-412 Testcase Example
Account Activity
The transactions throughout the month on the Account:
| 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)
Compounding period: Daily (365 in year) (1/365=0.0027397260273973)
Periodic interest rate i = 0.12 x 0.0027397260273973 = 0.0003287671232
Posting/Crediting period: monthly crediting period (n=12)
The formula is: Interest = Balance x periodic interest rate 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 (this period) | Total Interest Compounded |
|---|---|---|---|---|---|
| 26th Jan | 0 | 100,000 | 1 | 100,000 x 0.0003287671232 = 32.87671232 | 32.87671232 |
| 27th Jan | 100,000 | 0 | 1 | 0 + (32.87671232) x DR = 0.0108087821297204 | 32.887521102 |
| 28th Jan | 0 | 0 | 1 | 0 + (32.887521102) x DR = 0.0108123357018838 | 32.898333437 |
| 29th Jan | 0 | 0 | 1 | 0 + (32.898333437) x DR = 0.0108158904421569 | 32.909149327 |
| 30th Jan | 0 | 0 | 1 | 0 + (32.909149327) x DR = 0.010819446351197 | 32.919968773 |
| 31st Jan | 0 | 0 | 1 | 0 + (32.919968773) x DR = 0.010823003429333 | 32.930791776 |
| 0 | 31 | Total interest earned = 32.93 credited on 1st Feb 2013 | =32.93 (0.000791776 dropped) |