Summary (Grade 12 NSC Matric Mathematics): Revision Notes

Summary

Financial protection basics

When managing your money, it's crucial to understand the risks involved in different financial decisions. Financial protection means safeguarding your money by making informed choices about where and how you invest or store it.

Why is handing money over risky?

When you give your money (notes and coins) to another person who then loses, steals, or goes bankrupt with it, you only have an unsecured claim against that person or their estate. This means you might not get all your money back.

Why banks are safer

Banks and investment companies must be registered and regulated. This supervision ensures your money is safer than with unregulated persons or groups who don't follow these protective rules.

Bank regulation includes requirements for capital reserves, regular audits, deposit insurance schemes, and strict operational guidelines. These measures significantly reduce the risk of losing your money compared to unregistered entities.

Essential finance formulas

Understanding these formulas is critical for solving finance problems. Always ensure the interest rate and time period are in the same units.

Interest calculations

Simple interest grows in a straight line pattern:

• Formula: $A = P(1 + in)$
• Where A = final amount, P = principal, i = interest rate per period, n = number of periods

Compound interest grows exponentially as interest earns interest:

• Formula: $A = P(1 + i)^n$
• The interest compounds or builds upon itself each period

Depreciation calculations

Simple depreciation reduces value in a straight line:

• Formula: $A = P(1 - in)$
• Value decreases by the same amount each period

Compound depreciation reduces value exponentially:

• Formula: $A = P(1 - i)^n$
• Value decreases by the same percentage each period

Interest rate conversions

Nominal and effective annual interest rates are related by:

• Formula: $1 + i = (1 + i_{(m)}/m)^m$
• Where $i_{(m)}$ = nominal rate compounded m times per year
• This converts between different compounding frequencies

The effective annual rate is always higher than the nominal rate when compounding occurs more than once per year. This formula helps you compare different investment options with different compounding frequencies.

Payment calculations (annuities)

These formulas help calculate regular payment scenarios like loans or investments.

Future value of payments

When making regular payments into an investment:

• Future value formula: $F = x\frac{(1 + i)^n - 1}{i}$
• Payment amount formula: $x = F \times \frac{i}{(1 + i)^n - 1}$

This calculates what regular payments will be worth in the future, or what payment is needed to reach a target amount.

Present value of payments

When receiving regular payments or paying off a loan:

• Present value formula: $P = x\frac{1 - (1 + i)^{-n}}{i}$
• Payment amount formula: $x = P \times \frac{i}{1 - (1 + i)^{-n}}$

This calculates the current value of future payments, or what payment is needed to pay off a current debt.

Exam tips

Successful finance problem-solving requires a systematic approach and attention to detail.

• Always check units: Ensure interest rates and time periods match (monthly rate with monthly periods, annual rate with annual periods)
• Identify the type: Determine if you're dealing with simple or compound interest/depreciation
• Choose the right formula: Future value for growth scenarios, present value for current worth calculations
• Show all steps: Write out the formula, substitute values, then calculate