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N u m b e r Time Value of Money Formula For: Annual Compounding 1 Future Value of a Lump Sum. ( FVIFi,n ) F V = P V ( 1 + i )n 2 Present Value of a Lump Sum. ( PVIFi,n ) -n 3 Future Value of an Annuity. ( FVIFAi,n ) 4 Present Value of an Annuity. ( PVIFAi,n ) 5 Present Value of a Perpetuity. 6 Effective Annual Rate given the APR. EAR = APR 7 The length of time required for a PV to grow to a FV. ln (FV/PV) n= ln (1 + i ) 8 The APR required for a PV to grow to a FV. FV i= -1 PV Compounded (m) Times per Year i FV = PV 1 + m nm FV = PV(e )in - nm PV = FV ( 1 + i ) ( 1 + i )n - 1 FVA = PMT i 1 - ( 1 + i )- n PVA = PMT i PMT PVperpetuity i Continuous Compounding i PV = FV 1 + m 1 (i / m) nm 1 FVA PMT i/m 1 - 1 + (i / m) - nm PVA = PMT i/m PMT PVperpetuity [(1 i)1/ m 1] PV = FV( e )-in m 1/ n Legend i = the nominal or Annual Percentage Rate m = the number of compounding periods per year ln = the natural logarithm, the logarithm to the base e PMT = the periodic payment or cash flow i EAR = 1 + - 1 m n= ln ( FV/PV) i m * ln 1 m FV 1/(nm) i = m * - 1 PV EAR = e i - 1 n= 1 * ln ( FV/PV) i i= 1 * ln (FV/PV) n n = the number of periods EAR = the Effective Annual Rate e = the base of the natural logarithm ≈ 2.71828 Perpetuity = an infinite annuity Geographic buying power = City 1 Index Number x Salary)/City 2 Index Number Tax-equivalent of a nontaxable benefit = Value of the benefit/(1-Tax Rate) Net Worth = Total assets – Total liabilities Debt ratio = Liabilities/Net worth Current ratio = Liquid assets/Current liabilities Liquidity ratio = Liquid assets/Monthly expenses Debt-payments ratio = Monthly credit payments/Take-home pay Savings ratio = Amount saved per month/Gross monthly income Cash surplus (or deficit) = Total inflows – Total outflows APY = 100 x [(1 + Interest/Principal)365/days in term – 1] After-tax rate of return = Interest rate x (1 – Tax rate) APR = [2 x Number of payment periods in one year x Dollar cost of credit/Loan amount x (Total number of payments to pay off the loan + 1)] Simple interest (in dollars) = Principal borrowed x Interest rate x Length of loan in years Total future value of a loan = Principal x (1 + Rate of interest)Time in years Monthly payment = Loan x [Monthly interest rate x (1 + Monthly interest rate)Time in months/(1 + Monthly interest rate)Time in months - 1] Approximate market price = Annual interest amount/Comparable interest rate Earnings per share = After-tax income/Number of common stock shares outstanding Price-earnings (PE) ratio = Price per share/Earnings per share of stock Current yield = Annual income amount/Market value Total return = Current return + Capital gain Annualized holding period yield = (Total return/Original investment) x (1/N) Book value = (Assets – Liabilities)/Number of common stock shares outstanding Dollar amount of annual interest = Face value x Interest rate Approximate market value = Dollar amount of annual interest/Comparable interest rate Current yield for a 26-week T-bill = (Discount amount/Purchase price) x 2 Taxable equivalent yield = Tax-exempt yield/1.0 – Your tax rate Approximate YTM = [Dollar amount of annual interest + (Face value – Market value)/Number of periods]/[(Market value + Face value)/2] Net asset value = (Value of a funds portfolio – Liabilities)/ Number of shares outstanding Total return = Income dividends + Capital gains distributions + Change in market value Percent of total return = Dollar amount of total return/Original cost of investment