Financial managers constantly have to make decisions based on the time value of money concept; whether it is decisions about in which projects, the firm should invest its capital resources, or about how the firm should raise the capital resources necessary for its activities. Such decisions can only be made effectively and lead to an increase in the value of the firm if the financial manager has a sound understanding of the time value of money concept. The time value of money concept is thus extremely relevant to both investment and financing decisions. Not just to the investment and financing decisions of the firm, but also at a personal level for us all. For example, whether you are buying a house, joining a savings scheme, or providing for a future pension, the time value of money affects them all and consequently your personal wealth.

Annuities have a profound effect TVM problems and investment outcomes.

"An annuity is a special cash flow pattern in which, as its name implies a constant annual amount is to be paid or received over a defined number of years." (Metcalfe, 1995) An annuity due is one in which cash flows occur at the beginning of each year. Ordinary annuities are much more common than annuities due and from now on, unless otherwise stated, we will assume we are dealing with ordinary annuities. An annuity can be for any fixed annual amount and extend over any time period. They occur frequently in finance, particularly in the area of financial services (personal savings, investments, pensions, and trust funds management).

The future value of an annuity (FVA) is the total sum the annuity will be worth at the end of the annuity term, when a constant annual amount is invested each year and retained until the end of...