## Mathematics of finance

In this chapter, we introduce the reader to one of the most important concepts in finance – the time value of money. The concept of the time value of money answers such questions as the following. If $5000 is deposited in a savings account that earns interest at the annual rate of 12 percent, how much money will be in the account seven years from now? What is the present value of $3000 due in five years if the interest rate is 7 percent compounded quarterly? Would you rather have a savings account that pays 6 percent compounded annually or 5 percent compounded continuously? We show how to compute the present and future values of a stream of cash flows and how to compare the future results of an investment with its present cost. Certain types of assets, such as annuities and perpetuities, have cash flows that follow a regular pattern. We also discuss annuities, perpetuities, mortgages, car loans, student loans and the effective rate of interest.