This is a very practical and important lesson for your exam. It covers two advanced ways interest is calculated in real-world situations like bank loans, installment plans, and savings accounts.

1. Interest on the Reducing Balance

This method is commonly used for loans that are paid back in equal monthly installments (like for a TV or a motorbike).

The Core Idea: Instead of charging interest on the full loan amount for the entire period, interest is only calculated on the amount you still owe. As you pay installments, the amount you owe reduces, so the interest also reduces over time.

Key Formula: Number of Month Units

Calculating the interest month by month is slow. We use a shortcut by calculating the "number of month units". This represents the total number of loan portions that are subject to interest over the entire loan period.

Number of Month Units = n(n + 1) / 2 Where 'n' is the number of monthly installments.

• Example: For a 12-month loan, n=12. Number of month units = 12(12 + 1) / 2 = 12 * 13 / 2 = 78.

How to Calculate the Monthly Installment

Follow these steps exactly.

1. Calculate the Loan Amount: Loan Amount = Cash Price - Down Payment.

2. Calculate the Loan Portion per Month: Portion = Loan Amount / n (where 'n' is the number of months).

3. Calculate the Interest for one Month Unit: Interest per Unit = Portion × Monthly Interest Rate. (Remember: Monthly Rate = Annual Rate / 12).

4. Calculate the Total Interest: Total Interest = Interest per Unit × Number of Month Units.

5. Calculate the Total to be Repaid: Total Repaid = Loan Amount + Total Interest.

6. Calculate the Monthly Installment: Installment = Total Repaid / n.

2. Compound Interest

This method is commonly used for savings accounts or long-term loans.

The Core Idea: At the end of each period (usually a year), the interest earned is added to the principal amount. The interest for the next period is then calculated on this new, larger principal. This means you start earning "interest on your interest".

How to Calculate Compound Interest

The most reliable way is the year-by-year method.

1. Year 1:

   • Interest for Year 1 = Principal × Annual Rate

   • New Principal at end of Year 1 = Principal + Interest for Year 1

2. Year 2:

   • Interest for Year 2 = (New Principal at end of Year 1) × Annual Rate

   • New Principal at end of Year 2 = (New Principal at end of Year 1) + Interest for Year 2

3. Continue for the required number of years.

Shortcut Formula (for checking your answer): Total Amount = Principal × (1 + Rate/100)ⁿ Where 'n' is the number of years.

Exam Tips & Common Mistakes

• Mistake 1 (Reducing Balance): Using the annual interest rate instead of the monthly rate. Always divide the annual rate by 12 first.

• Mistake 2 (Reducing Balance): Forgetting to subtract the down payment. The loan is only for the remaining balance.

• Mistake 3 (Compound Interest): Calculating simple interest for all years and adding it at the end. The key to compound interest is that the principal grows each year.

• Exam Tip 1: When a question asks you to find the annual interest rate for a reducing balance loan, you have to work backwards.

  1. Find the total amount paid (Installment × n).

  2. Find the total interest (Total Paid - Loan Amount).

  3. Find the interest for one month unit (Total Interest / Number of Month Units).

  4. Use this to find the interest rate: Rate = (Interest per Unit / Portion) × 100% × 12.

• Exam Tip 2: For comparison questions ("Which is better, simple or compound interest?"), calculate the final amount for both scenarios and write a concluding sentence stating which is better and by how much. For a saver, compound interest is better. For a borrower, simple interest is better.