Financial and Business Mathematics
This domain tests simple and compound interest, annuities, and bill discounting - areas where a single formula slip loses the whole mark.
Interest
Simple interest SI = PRT/100. Compound amount A = P(1 + i)ⁿ, where i is the rate per conversion period and n the number of such periods; for half-yearly compounding, i = r/2 and n = 2t. Compound interest = A − P.
Annuities
For a regular payment A at the end of each period, n periods, rate i per period:
- Future value (ordinary annuity) FV = A[(1 + i)ⁿ − 1]/i.
- Present value PV = A[1 − (1 + i)^(−n)]/i.
Bill discounting
- Banker's discount BD = face value × r × t, always computed on the face value.
- True discount TD = FV·r·t/(1 + rt), computed on the present value.
- Banker's gain BG = BD − TD.
Worked example
₹2000 is deposited at the end of each year for 3 years at 10% compounded annually. FV = 2000[(1.1)³ − 1]/0.10 = 2000(1.331 − 1)/0.10 = 2000 × 3.31 = ₹6620. For a bill of face value ₹10,000 discounted 6 months at 10% p.a.: BD = 10000 × 0.10 × 0.5 = ₹500, while TD = 500/1.05 = ₹476.19, so banker's gain = ₹23.81.
Traps that cost marks
- Entering time in months where the formula needs years (6 months = 0.5 year).
- Using the annual rate with half-yearly compounding without halving the rate and doubling the periods.
- Computing banker's discount on the present value instead of the face value - this swaps BD and TD.
- Treating an annuity-due (payment at the start) with the ordinary annuity formula, which understates it by one period of interest.