SUMMARY

The mathematics of individual finance deals with the time value of money. Financial planning involves looking at financial flows and balances in the future which are subject to the compounding of interest over time. In this chapter we reviewed a number of different ways of making these calculations. Some can be done arithmetically, while others are more efficiently done with the use of financial calculators, financial tables and spreadsheets.

Four basic calculations comprise the mathematics of individual finance. These are the future value of a present sum of money, the present value of a future sum, the future value of an annuity and the present value of an annuity. It is important to distinguish between an annuity, where payments are made at the end of each period, and an annuity due, where payments are made at the beginning of each period. Conversion from an annuity to an annuity due is mathematically simple and the conversion process is necessary when dealing with financial tables or spreadsheets. Most financial calculators will perform this conversion for the user.

Valuation of a bond is a combination of a simple annuity and the present value of the repayment of principal at maturity. Amortized loans are simple annuities.

Valuation can also be used to value household investments. These may be physical investments such as a washer and dryer or they can be investments in human capital, such as additional schooling.

The choice of an appropriate discount rate depends upon many things including the amount of risk, the duration of the payments and the return on bonds of similar duration.