Financial Mathematics: Interest, Depreciation and Annuities
What you must understand
Financial mathematics covers simple interest, compound interest, appreciation and depreciation, and loans and investments modelled by recurrence relations or annuity formulas. You need the simple interest formula I = Prn, the compound interest formula A = P(1 + r)ⁿ, and the idea that r must be expressed as a decimal rate per compounding period. Depreciation can be straight-line (constant amount) or declining-balance (a fixed percentage each year). You should also interpret a recurrence relation such as Vₙ₊₁ = Vₙ(1 + r) + d, which models regular deposits or repayments, and use tables or technology to find unknown values.
Traps to watch
- Rate per period: an annual rate of 6% compounded monthly means r = 0.06/12 = 0.005 and n = 12 × years. Forgetting to divide the rate is the most frequent error.
- Time in years versus periods: n counts compounding periods, not years.
- Simple versus compound: simple interest is calculated on the original principal only.
- Depreciation direction: declining balance multiplies by (1 − r); straight-line subtracts a fixed amount.
- Rounding money: round only at the final step, and give cents where appropriate.
Worked example
$5000 is invested at 4.8% per annum compounding quarterly for 3 years. r = 0.048/4 = 0.012 and n = 12. A = 5000(1.012)¹² ≈ $5772.79. Interest earned ≈ $772.79.
Rule of thumb
For any compounding question, first write down r per period and n periods, then substitute. For recurrence models, track the value year by year using a table.