...
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:
...
| 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 Balance Method
Compound Interest Forumula using in Daily Compounding:
...
| Date | Up to & (inclusive) | Days | Type | Amount | Opening Bal | Closing Bal | Interest on Bal | Interest To Date | Bal for Compounding | (I) Posted |
|---|---|---|---|---|---|---|---|---|---|---|
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 | |
| 01/04/13 | 30/06/2013 | 91 | No activity | 3.40 | 800 | 800 | 10.077033616 | 13.481773247 | 813.481773247 | Interest earned but not yet posted |
Compound Interest Forumula
...
used in Monthly Compounding:
The interest earned on a savings account balance on a given end of day is calculated using the following:
...
| Note | ||
|---|---|---|
| ||
The frequency of the posting period makes no difference (or neglible difference) to the interest earned on the savings account when using compound interest. But the compounding periods do. Not the slight different in interest earned for monthly compounding versus daily. |
Monthly Compounding
...
- Monthly Posting using Daily Balance Method
afdafa
afda
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).
...
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)
| Date | Up to & (inclusive) | Days | Type | Amount | Opening Bal | Closing Bal | Interest on Bal | Interest To Date | Balance For Compounding |
|---|---|---|---|---|---|---|---|---|---|
01/03/2013 | 01/03/2013 | 1 | Deposit | 1200 | 0 | 1200 | 0.164383562 | 0.164383562 | |
| 02/03/2013 | 09/03/2013 | 8 | Withdrawal | 100 | 1200 | 1100 | 1.206237813 | 1.370621375 | |
| 10/03/2013 | 14/03/2013 | 5 | Withdrawal | 400 | 1100 | 700 | 0.480522469 | 1.851143844 | |
| 15/03/2013 | 15/03/2013 | 1 | Deposit | 200 | 700 | 900 | 0.123541253 | 1.974685097 | |
| 16/03/2013 | 17/03/2013 | 2 | Withdrawal | 900 | 900 | 0 | 0.000541047 | 1.975226144 | |
| 18/03/2013 | 20/03/2013 | 3 | Deposit | 200 | 0 | 200 | 0.083014888 | 2.058241032 | |
| 21/03/2013 | 30/03/2013 | 10 | Deposit | 700 | 200 | 900 | 1.236458229 | 3.294699261 | |
| 31/03/2013 | 31/03/2013 | 1 | Withdrawal | 100 | 900 | 800 | 0.110040370 | 3.404739631 | 803.404739631 |
| End of posting period | 31 | 3.40 to be posted | |||||||
| 01/04/13 | 30/04/2013 | 30 | Interest Posting | 3.40 | 800 | 803.40 | 3.308210288 | 3.308210288 | 806.797260274 |
| 01/05/13 | 31/05/2013 | 31 | none | 0 | 803.40 | 803.40 | 3.432803347 | 6.727356165 | 810.001643836 |
| 01/06/13 | 30/06/2013 | 30 | none | 0 | 803.40 | 803.40 | 3.335964006 | 10.056657535 | 813.555712329 |
| End of posting period | 91 | 10.06 to be posted | |||||||
| Total | 122 | 13.46 posted | |||||||
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