Download Time Value of Money Formula For

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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
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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