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:

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:

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)

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)

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)

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).

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:

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).