Chapter 55. Mathematics of Finance

PAMELA P. DRAKE, PhD, CFA

J. Gray Ferguson Professor of Finance and Department Head of Finance and Business Law, James Madison University

FRANK J. FABOZZI, PhD, CFA, CPA

Professor in the Practice of Finance, Yale School of Management

Abstract: Investment and financing decisions require the valuation of investments and the determination of yields on investments. Necessary for the valuation and yield determination are the financial mathematics that involve the time value of money. With these mathematics, we can translate future cash flows to a value in the present, translate a value today into a value at some future point in time, and calculate the yield on an investment. The time-value-of-money mathematics allow the financial decision-maker to evaluate and compare investments and financing arrangements.

Keywords: time value of money, simple interest, compound interest, interest on accumulated interest, interest on interest, growth rate, return, arithmetic average return, geometric average return, compound average annual return, true return, annual percentage rate, continuous compounding, discount factor, ordinary annuity, future value annuity factor, present value annuity factor, loan amortization, perpetuity, annuity due, deferred annuity, nominal interest rate, annual percentage rate, effective annual rate, loan amortization, fully amortizing loan, amortization, balloon payments, yield, internal rate of return

THE IMPORTANCE OF THE TIME VALUE OF MONEY ...

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