Financial Mathematics
Applied Mathematics, Unit VII. Covers Perpetuity and sinking funds; EMI; Rate of return and CAGR; Linear depreciation; Bond valuation.
About this unit
Financial Mathematics applies the ideas of interest and present value to everyday money decisions. The unit covers perpetuities (payments that continue for ever) and sinking funds (regular savings to meet a future liability), the equated monthly instalment (EMI) used to repay loans, the nominal rate of return and the compound annual growth rate (CAGR) for judging investments, straight-line (linear) depreciation of assets, and the valuation of bonds as the present value of their future cash flows. The common tool is the time value of money: a rupee today is worth more than a rupee in the future, so future amounts are discounted to compare them fairly.
How to prepare
- Learn the formulas: perpetuity PV = R/i; sinking fund payment = A·i/[(1 + i)ⁿ − 1]; EMI = P·i(1 + i)ⁿ/[(1 + i)ⁿ − 1]; CAGR = (FV/BV)^(1/n) − 1; annual depreciation = (cost − residual value)/useful life; bond value = PV of coupons + PV of face value.
- Always convert the annual rate to the rate per period (monthly i = annual rate/12).
- Practise with a calculator-free approach on small numbers and learn to estimate answers.
Topics in this chapter
Perpetuity and sinking funds
Calculating perpetuities and sinking funds.
5 questionsEMI
Calculating equated monthly instalments.
5 questionsRate of return and CAGR
Nominal rate of return and compound annual growth rate.
5 questionsLinear depreciation
Cost, residual value and useful life.
5 questionsBond valuation
Bond terms and present-value valuation.
5 questions