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 compounding period used.
The interest compounding period is the span of time at the end of which savings in a client’s account earn interest. Interest periods may vary; they may be daily, weekly, bi-weekly, monthly, quarterly, semi-annual or annual.
Examples of each method are provided using account activity for one month and the interest is calculated at the end of the day, end of the month - 31st Mar 2013
Account Activity
The client makes the following transactions throughout the month:
| 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