Financial Mathematics
What the exam tests
Financial mathematics questions apply simple and compound interest, effective rates, annuities, present value and depreciation. The arithmetic is simple; the marks are lost by misreading whether the rate is per annum, whether compounding is annual or periodic, and whether the annuity is ordinary or due.
Core rules
- Simple interest: I = Pnr/100; amount A = P(1 + nr/100).
- Compound interest: A = P(1 + r/100)ⁿ; for compounding m times a year, A = P(1 + r/(100m))^(mn).
- Effective annual rate: r_eff = (1 + r/m)^m − 1.
- Present value of an ordinary annuity: PV = C[1 − (1 + i)^(−n)]/i, where i is the rate per period.
- Future value of an ordinary annuity: FV = C[(1 + i)ⁿ − 1]/i.
Worked example
Find the compound interest on ₹10,000 at 10% per annum for 2 years, compounded annually. A = 10,000(1 + 0.10)² = 10,000 × 1.21 = ₹12,100. CI = 12,100 − 10,000 = ₹2,100.
Present value check: ₹1,000 received at the end of each year for 3 years at 10%. PV = 1000[1 − (1.1)^(−3)]/0.1 = 1000(1 − 0.751315)/0.1 = 1000 × 2.48685 = ₹2,486.85.
Traps
- Entering 10 instead of 0.10 in the compound formula, or vice versa.
- Counting 2 years of annual compounding as 3 periods.
- Using the future-value annuity formula when the question asks for present value.
- Treating an annuity due as an ordinary annuity; an annuity due is worth (1 + i) times more.
- Subtracting the principal from the amount only when the question asks for interest, not the amount.