Interest Calculation and Compounding

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:

  1. The daily balance method; and
  2. 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:

DateTransactionAmount
01 Mar 2013Deposit1200
02 Mar 2013Withdrawal100
10 Mar 2013Withdrawal400
15 Mar 2013Deposit200
16 Mar 2013Withdrawal900
18 Mar 2012Deposit200
21 Mar 2012Deposit700
31st Mar 2013Withdrawal100

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)

 

DateUp to & (inclusive)DaysTypeAmountOpening BalClosing BalInterest on BalInterest To DateBal for Compounding(I) PostedGain/Loss Due To Rounding

01/03/2013

01/03/20131Deposit1200012000.1643835620.1643835621200.164383562  
02/03/201309/03/20138Withdrawal100120011001.2062378131.3706213751,101.370621375  
10/03/201314/03/20135Withdrawal40011007000.4805224691.851143844701.851143844  
15/03/201315/03/20131Deposit2007009000.1235412531.974685097901.974685097  
16/03/201317/03/20132Withdrawal90090000.0005410471.9752261441.975226144  
18/03/201320/03/20133Deposit20002000.0830148882.058241032202.058241032  
21/03/201330/03/201310Deposit7002009001.2364582293.294699261903.294699261  
31/03/201331/03/20131Withdrawal1009008000.1100403703.404739631803.4047396313.40-0.004739631
01/04/1330/04/201330Interest Posting3.40800803.403.3082102883.308210288806.7082102883.31+0.001789712
01/05/1331/05/201331Interest Posting3.31803.40806.713.4328033473.432803347810.1428033473.43-0.002803347
01/06/1330/06/201330Interest Posting3.43806.71810.143.3359640063.335964006813.4759640063.34+0.004035994
  122   813.48   13.48Loss 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)

 

DateUp to & (inclusive)DaysTypeAmountOpening BalClosing BalInterest on BalInterest To DateBal for Compounding(I) PostedGain/Loss Due To Rounding

01/03/2013

01/03/20131Deposit1200012000.1643835620.1643835621200.164383562  
02/03/201309/03/20138Withdrawal100120011001.2062378131.3706213751,101.370621375  
10/03/201314/03/20135Withdrawal40011007000.4805224691.851143844701.851143844  
15/03/201315/03/20131Deposit2007009000.1235412531.974685097901.974685097  
16/03/201317/03/20132Withdrawal90090000.0005410471.9752261441.975226144  
18/03/201320/03/20133Deposit20002000.0830148882.058241032202.058241032  
21/03/201330/03/201310Deposit7002009001.2364582293.294699261903.294699261  
31/03/201331/03/20131Withdrawal1009008000.1100403703.404739631803.4047396313.40-0.004739631
01/04/1330/06/201391Interest Posting3.40800803.40   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)

 

DateUp to & (inclusive)DaysTypeAmountOpening BalClosing BalInterest on BalInterest To DateBal for Compounding(I) Posted

01/03/2013

01/03/20131Deposit1200012000.1643835620.1643835621200.164383562 
02/03/201309/03/20138Withdrawal100120011001.2062378131.3706213751,101.370621375 
10/03/201314/03/20135Withdrawal40011007000.4805224691.851143844701.851143844 
15/03/201315/03/20131Deposit2007009000.1235412531.974685097901.974685097 
16/03/201317/03/20132Withdrawal90090000.0005410471.9752261441.975226144 
18/03/201320/03/20133Deposit20002000.0830148882.058241032202.058241032 
21/03/201330/03/201310Deposit7002009001.2364582293.294699261903.294699261 
31/03/201331/03/20131Withdrawal1009008000.1100403703.404739631803.404739631 
01/04/1330/06/201391No activity3.4080080010.077033616 13.481773247813.481773247Interest 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)

DateUp to & (inclusive)DaysTypeAmountOpening BalClosing BalInterest on BalInterest To DateBalance For Compounding

01/03/2013

01/03/20131Deposit1200012000.1643835620.164383562 
02/03/201309/03/20138Withdrawal100120011001.2062378131.370621375 
10/03/201314/03/20135Withdrawal40011007000.4805224691.851143844 
15/03/201315/03/20131Deposit2007009000.1235412531.974685097 
16/03/201317/03/20132Withdrawal90090000.0005410471.975226144 
18/03/201320/03/20133Deposit20002000.0830148882.058241032 
21/03/201330/03/201310Deposit7002009001.2364582293.294699261 
31/03/201331/03/20131Withdrawal1009008000.1100403703.404739631803.404739631
End of posting period31     3.40 to be posted 
01/04/1330/04/201330Interest Posting3.40800803.403.3082102883.308210288806.797260274
01/05/1331/05/201331none0803.40803.403.4328033476.727356165810.001643836
01/06/1330/06/201330none0803.40803.403.33596400610.056657535813.555712329
End of posting period91     10.06 to be posted 
Total122     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