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 Balance Method

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:

Compounding Interest Formula

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

The frequency of the posting period makes no difference (or neglible difference) to the interest earned on the savings account when using compound interest. See the break down of the account activity with monthly, quarterly and yearly posting frequencies.

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)

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	Loss of 0.003506984

Daily Compounding - Quarterly Posting Using Daily Balance Method

The account activity breaks down into the following End of Day Balances:

Quarterly Posting so we want to post interest to the account for periods (01 Jan - 31 Mar), (01 Apr - 30 Jun)

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	30/06/2013	91	Interest Posting	3.40	800	803.40				10.08
		122				813.48				13.48

Daily Compounding - Annual Posting Using Daily Balance Method

The account activity breaks down into the following End of Day Balances:

Annual Posting so we want to post interest to the account for periods (01 Jan - 31 Dec)

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:

Compounding Interest Formula

A= Prn where,

P = 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.

Compounding Periods Matter

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

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

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