Personal Financial Management
Core concepts
Personal finance questions ask you to model money over time. You must be fluent with simple and compound interest, the reducing-balance loan, annuity and amortisation formulas, inflation and purchasing power, and taxation, PAYG and net pay. Know the difference between a nominal rate quoted per year and the periodic rate applied each compounding period: divide the annual rate by the number of periods per year, and remember the number of periods is years × periods-per-year.
Traps to watch
- Compounding frequency mismatch: a question may quote 6% p.a. compounding monthly but ask for a quarterly payment. Convert carefully.
- Rounding the interest before subtracting the repayment - always calculate interest on the opening balance, then subtract the payment, and round only the final answer unless told otherwise.
- Sign conventions: money borrowed is positive to the borrower, negative to the lender; be consistent.
- Effective vs nominal rates: use (i_{\text{eff}}=(1+r/n)^n-1) when comparing products.
- Depreciation: straight-line vs declining-balance - declining-balance uses the same compound formula with a negative rate.
Worked rule of thumb
For a reducing-balance loan of (P) dollars at periodic rate (i) over (n) periods, the repayment is [R=\frac{P,i}{1-(1+i)^{-n}}.] Example: borrow $20 000 at 6% p.a. compounding monthly for 5 years. Here (i=0.005), (n=60). Then (R=\frac{20000(0.005)}{1-(1.005)^{-60}}\approx\frac{100}{1-0.7414}\approx$386.66). Check: total repaid ≈ $23 200, so total interest ≈ $3 200 - plausible for a 5-year loan. Always sanity-check that total repayments exceed the principal but not absurdly.