Bank accounts are offered by certain financial institutions that allow people to deposit and withdraw money which can earn interest.

## Interest on Bank Accounts

Most banks offer interest on their bank accounts. The amount of interest offered depends on the amount in the account, the time it will be invested for and whether you will withdraw funds from the account. There are two ways banks can calculate interest that is covered in this unit- minimum monthly balance and daily balance.

## Minimum Monthly Balance

Interest is calculated on minimum monthly balance accounts by finding the smallest account balance for that month which interest is calculated upon.

### Example 1

The following table shows all of the transactions that occurred in May. The bank pays 4% p.a. simple interest on the minimum monthly balance.

 Date Deposit Withdrawal Balance 3/5 $0.91$424.50 8/5 $150$574.50 16/5 $20$594.50 22/5 $282.50$312 29/5 $55$367

Find the interest that will be earned in May.

We are told that interest is calculated on the minimum monthly balance so we need to find this first. Look through the figures in the ‘balance’ column to locate the smallest amount. Note that the opening balance has not been provided so you need to calculate and check whether this is the smallest amount.

Minimum monthly balance for May is $312. Write down the values provided and substitute these into the simple interest formula. $P=312$ $r=\frac 4{12}=\frac 14$% per month $T=1$ $I=\frac {PrT}{100}$ $I=\frac {312\times \frac {1}{4} \times 1}{100}$ $I=0.78$ The interest earned in May is$0.78.

## Daily Balance

As given by the name, to calculate interest using this method a bank will find the balance of the account each day and calculates interest on that balance.

### Example 2

A bank pays 6% p.a. simple interest on the daily balance of the account shown below.

 Date Deposit Withdrawal Balance 3/5 $0.91$424.50 8/5 $150$574.50 16/5 $20$594.50 22/5 $282.50$312 29/5 $55$367

How much interest will be earned in May?

Make a table with each new balance, the number of days the balance applies for, room for the calculations and interest earned.

 Balance Days* Calculation** Interest*** $423.59 2 $\frac {423.59\times 6\times \frac 2{365}}{100}$$0.13926 $424.50 5 $\frac {424.5\times 6\times \frac 5{365}}{100}$$0.34890 $574.50 8 $\frac {574.5\times 6\times \frac 8{365}}{100}$$0.75555 $594.50 6 $\frac {594.5\times 6\times \frac 6{365}}{100}$$0.58636 $312 7 $\frac {312\times 6\times \frac 7{365}}{100}$$0.35901 $367 3 $\frac {367\times 6\times \frac 3{365}}{100}$$0.18099

*Days: to find the amount of days, use the day count on your calculator. Make sure your settings are for the Australian (not American) date format. Also check that the amount of days you have equals the amount of days in that month.

**Calculation: this is just the simple interest formula where $T$ is the amount of days divided by 365.

***Interest: add all of the interest payments together to find total interest for that month. Make sure to round to at least hundredths of a cent for accuracy.

Interest $=0.13926+0.34890+0.75555+0.58636+0.35901+0.18099$
Interest $=2.37007$

There was \$2.37 interest earned during May.