Amortisation Tables Revision Notes for VCE SSCE General Mathematics

Amortisation Tables

What are amortisation tables?

Amortisation tables are detailed schedules that show exactly what happens with each payment you make on a loan, annuity, or investment. Rather than just showing the final balance after each payment, these tables break down every transaction to show:

How much you pay or receive
How much goes towards interest
How much reduces (or increases) the principal
What the new balance is after each payment

This level of detail helps you understand exactly where your money is going and how your loan balance decreases (or investment grows) over time.

infoNote

The term amortisation comes from accounting and refers to the process of gradually paying off a debt or building up an investment through regular payments. An amortisation table provides a complete record of this process, showing the status after each transaction.

Amortisation tables for reducing balance loans

Understanding amortising loans

An amortising loan is a loan that you pay off completely by making regular payments over time. Each payment you make serves two purposes:

Paying the interest charged on the remaining loan balance
Reducing the principal (the amount you originally borrowed)

As you make more payments, the amount owing decreases, which means the interest charges also decrease. This allows more of each payment to go towards reducing the principal.

How loan payments are allocated

Let's look at how a payment is split up. Consider a loan of $1000 with an interest rate of 15% per year, paid back with monthly payments of $250.

The process works like this:

Step 1: Calculate the interest charged

First, work out the interest rate per compounding period. Since interest is charged monthly, divide the annual rate by 12:

$\text{Monthly rate} = \frac{15\%}{12} = 1.25\%$

Then calculate the interest on the current balance:

$\text{Interest} = 1000 \times 1.25\% = \$12.50$

Step 2: Calculate the principal reduction

This is the amount of your payment that actually reduces the loan:

$\text{Principal reduction} = \text{Payment} - \text{Interest} = 250 - 12.50 = \$237.50$

Step 3: Calculate the new balance

Subtract the principal reduction from the previous balance:

$\text{New balance} = 1000 - 237.50 = \$762.50$

chatImportant

The calculation order is critical: Always calculate interest first using the previous balance, then find the principal reduction, and finally calculate the new balance. Doing these out of order will give you incorrect results.

Structure of an amortisation table

An amortisation table presents this information in an organised format:

Payment number	Payment	Interest	Principal reduction	Balance
0	0.00	0.00	0.00	1000.00
1	250.00	12.50	237.50	762.50

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Notice that row 0 shows the initial loan amount before any payments are made. This provides the starting point for all subsequent calculations.

Worked example: Constructing a loan amortisation table

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Worked Example: Building an Amortisation Table

Question: Flora borrows $20,000 at an interest rate of 8% per annum, compounding annually. She makes annual payments of $2500. Construct an amortisation table for the first three payments.

Solution:

For the first payment:

Calculate the interest on the initial balance:

$\text{Interest} = \frac{8}{100 \times 1} \times 20000 = \$1600.00$

Calculate the principal reduction:

$\text{Principal reduction} = 2500 - 1600 = \$900.00$

Calculate the new balance:

$\text{New balance} = 20000 - 900 = \$19100.00$

Repeat this process for the next two payments:

Payment number	Payment	Interest	Principal reduction	Balance
0	0.00	0.00	0.00	20,000.00
1	2500.00	1600.00	900.00	19,100.00
2	2500.00	1528.00	972.00	18,128.00
3	2500.00	1450.24	1049.76	17,078.24

Key observation: Notice how the interest decreases with each payment while the principal reduction increases. This is because the balance owing is getting smaller.

Worked example: Analysing a loan amortisation table

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Worked Example: Finding Missing Values

Question: A business borrows $10,000 at a rate of 8% per annum, compounding quarterly. The loan is repaid with quarterly payments of $2700.00. Some entries are missing from the amortisation table below:

Payment number	Payment	Interest	Principal reduction	Balance
0	0.00	0.00	0.00	10,000.00
1	2700.00	?	2500.00	7500.00
2	2700.00	150.00	?	4950.00
3	2700.00	99.00	2601.00	?

Calculate the missing values.

Solution:

Part a: Interest for payment 1

Calculate the quarterly interest rate:

$\text{Quarterly rate} = \frac{8}{100 \times 4} = 2\%$

Calculate the interest on the initial balance:

$\text{Interest} = 2\% \times 10000 = \$200.00$

Alternatively, since we know the payment ($2700) and the principal reduction ($2500):

$\text{Interest} = 2700 - 2500 = \$200.00$

Part b: Principal reduction for payment 2

$\text{Principal reduction} = 2700 - 150 = \$2550.00$

Part c: Balance after payment 3

$\text{New balance} = 4950 - 2601 = \$2349.00$

Amortisation tables for annuities

An annuity is the opposite of a loan - instead of making payments to pay off a debt, you receive regular payments that reduce a lump sum over time. The amortisation table structure is very similar to a loan table, but here you're tracking how regular withdrawals reduce your investment balance.

Each row shows:

The payment you receive
The interest earned on the remaining balance
How much the principal is reduced
The new balance

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While annuities work in reverse compared to loans (you receive money instead of paying it), the mathematical structure of the table remains the same. Both show how regular transactions affect a principal balance over time.

Worked example: Finding the interest rate from an annuity table

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Worked Example: Calculating Interest Rate from an Annuity

Question: Consider the following amortisation table for an annuity with monthly payments:

Payment number	Payment	Interest	Principal reduction	Balance
0	0.00	0.00	0.00	12,000.00
1	2200.00	60.00	2140.00	9860.00
2	2200.00	49.30	2150.70	7709.30
3	2200.00	A	B	5547.85

Part a: State the principal and the interest paid in the first month.

Solution:

From the table: Principal = $12,000, Interest = $60.00

Part b: Calculate the monthly interest rate.

Solution:

$\text{Monthly rate} = \frac{\text{Interest}}{\text{Principal}} \times 100 = \frac{60}{12000} \times 100 = 0.5\% \text{ per month}$

Part c: Find the values of A and B.

Solution:

Calculate A (interest on the balance from row 2):

$A = \frac{0.5}{100} \times 7709.30 = \$38.55$

Calculate B (principal reduction):

$B = 2200 - 38.55 = \$2161.45$

Amortisation tables for compound interest investments with additions

When you make regular deposits into an investment account that earns compound interest, the amortisation table works differently. Instead of reducing the balance, each payment increases the principal.

The key differences are:

Principal increase (not reduction): This equals the payment plus the interest earned
Balance increases with each payment
Formula: New balance = Previous balance + Principal increase

chatImportant

Critical difference for investments: Unlike loans where payments reduce the balance, in investment accounts both the deposit and the interest earned add to the principal. This means the balance grows with each payment rather than decreasing.

Worked example: Investment with regular deposits

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Worked Example: Investment with Monthly Additions

Question: Consider an amortisation table for a compound interest investment with monthly additions. The table shows:

Payment number	Payment	Interest	Principal increase	Balance
0	0.00	0.00	0.00	1200.00
1	50.00	3.00	53.00	1253.00
2	50.00	3.13	53.13	1306.13
3	50.00	3.27	53.27	1359.40

Complete two additional rows for payments 4 and 5.

Solution:

First, calculate the monthly interest rate:

$\text{Monthly rate} = \frac{3}{1200} \times 100 = 0.25\%$

For payment 4:

Calculate interest on the previous balance:

$\text{Interest} = 0.25\% \times 1359.40 = \$3.40$

Calculate the principal increase:

$\text{Principal increase} = 3.40 + 50 = \$53.40$

Calculate the new balance:

$\text{New balance} = 1359.40 + 53.40 = \$1412.80$

For payment 5:

Calculate interest:

$\text{Interest} = 0.25\% \times 1412.80 = \$3.53$

Calculate the principal increase:

$\text{Principal increase} = 3.53 + 50 = \$53.53$

Calculate the new balance:

$\text{New balance} = 1412.80 + 53.53 = \$1466.33$

Payment number	Payment	Interest	Principal increase	Balance
4	50.00	3.40	53.40	1412.80
5	50.00	3.53	53.53	1466.33

Key formulas for amortisation tables

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Essential Formulas for All Amortisation Tables

For reducing balance loans:

$\text{Interest paid} = \frac{r}{100 \times p} \times \text{previous balance}$

where $r$ = annual interest rate and $p$ = number of compounding periods per year

$\text{Principal reduction} = \text{Payment} - \text{Interest}$

$\text{New balance} = \text{Previous balance} - \text{Principal reduction}$

For compound interest investments with additions:

$\text{Interest earned} = \frac{r}{100 \times p} \times \text{previous balance}$

$\text{Principal increase} = \text{Interest} + \text{Payment}$

$\text{New balance} = \text{Previous balance} + \text{Principal increase}$

To find interest rate from a table:

$\text{Interest rate per period} = \frac{\text{Interest}}{\text{Principal}} \times 100$

Remember!

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Key Points to Remember:

Amortisation tables break down each payment to show interest, principal changes, and the new balance
For reducing balance loans, each payment reduces the balance. As the balance decreases, interest charges decrease and more of each payment goes towards principal reduction
For annuities, regular payments reduce a lump sum over time, similar to loans
For compound interest investments with additions, regular deposits increase the balance. Both the deposit and the interest earned add to the principal
Always calculate interest first using the previous balance, then find the principal reduction (or increase), and finally calculate the new balance
The first row (payment 0) always shows the initial amount before any payments are made

Amortisation Tables (VCE SSCE General Mathematics): Revision Notes