Mathematics of Finance
Mathematics of finance applies progressions to interest, annuities and valuation. The exam tests conversion of rates to the compounding period, the difference between simple and compound interest, and the present and future value of ordinary annuities.
Core rules
- Simple interest: I = Prt; amount A = P(1 + rt).
- Compound interest: A = P(1 + i)^n, where i = r/m is the rate per compounding period and n = mt is the number of periods.
- Effective annual rate: (1 + r/m)^m − 1, used to compare nominal rates with different compounding frequencies.
- Ordinary annuity (payments at period end): future value FV = R[((1 + i)^n − 1)/i]; present value PV = R[(1 − (1 + i)^−n)/i]. For an annuity due, multiply by (1 + i).
- Present value answers “what lump sum today is equivalent?”; future value answers “what will a stream accumulate to?”
Worked example
₹5,000 is invested at 8% nominal interest compounded quarterly for 2 years. The quarterly rate is i = 0.08/4 = 0.02 and the number of quarters is n = 4 × 2 = 8. A = 5,000(1.02)^8. Now (1.02)^8 = 1.171659, so A = ₹5,858.30 (to the nearest paisa). Simple interest at 8% for 2 years would give 5,000(1 + 0.08 × 2) = ₹5,800, so quarterly compounding adds ₹58.30. The gap is small here but grows with the rate and the time horizon.
Traps
- Using the annual rate directly when compounding is quarterly or monthly.
- Mismatching time units: 2 years with n = 8 quarters is correct only if i is the quarterly rate.
- Applying the annuity-due formula to payments made at the end of each period.
- Rounding intermediate powers too early.