Discrete Compounding Cash Flow Formulas
Discrete payments compounding equations and online calculators .
Single Payment
Compound Amount
Converts a single payment (or value) today  to a future value.
F = P [(1 + i)^{n}] (1)
where
F = future value
P = single payment today
i = interest rate per period
n = number of periods
Download and print Future Value of Present Payment chart
Example  Future Value of an Initial Amount Received Today
An amount of 5000 is received today. Calculate the future value of this amount after 7 years with interest rate 5%.
The interest rate can be calculated
i = (5 %) / /100 %)
= 0.05
The future value of the amount can be calculated
F = (5000) [(1 + 0.05)^{7}]
= 7036
Future Value  Online Calculator
Note that interest rate in % is used in the calculator  not in the equation.
Present Worth (or Value)
Converts a future payment (or value)  to present wort (or value).
P = F [(1 + i)^{n}] (2)
where
P = present value
F = single future payment
i = discount rate per period
n = number of periods
Download and print Present Value of Future Payment chart
Example  Present Value of a Future Payment
An payment of 5000 is received after 7 years. Calculate the present worth (or value) of this payment with dicount rate 5%.
The discount rate can be calculated
i = (5 %) / /100 %)
= 0.05
The present worth of the future payment can be calculated
F = (5000) [(1 + 0.05)^{7}]
= 3553
Present Value  Online Calculator
Note that discount rate in % is used in the calculator  not in the equation.
Uniform Series
Compound Amount  Annuity
Converts a uniform amount (annuity)  to a future value.
F = A [((1 + i)^{n}  1) / i ] (3)
where
F = future value
A = uniform amount per period
i = interest rate
n = numbers of periods
Download and print Compound Ammount of Uniform Annuity chart
Example  Present Value of Uniforms Payments
An uniform amount of 5000 is paid every year in 7 years. Calculate the future value of this amount with interest rate 5%.
The interest rate can be calculated
i = (5 %) / /100 %)
= 0.05
The future value of the annuity can be calculated
F = 5000 [((1 + 0.05)^{7}  1 ) / 0.05]
= 40710
Compound Amount  Online Calculator
Note that interest rate ín % is used in the calculator  not in the equation.
Sinking Fund
Converts a specific future value to uniform amounts (annuities).
A = F [i / ((1 + i)^{n}  1)] (4)
where
A = uniform amount per period
F = future value
i = interest rate
n = number of periods
Download and print Sinking Fund  Uniform Annuity to Future Value chart
Example  Uniforms Payments required to reach a Future Value
The future value of a 7 years annuity is 5000. Calculate the required annuity to reach this value with interest rate 5%.
The interest rate can be calculated
i = (5 %) / /100 %)
= 0.05
The uniform payments (annuity) can be calculated
A = 5000 [0.05 / ((1 + 0.05)^{7}  1)]
= 614
Sinking Fund  Online Calculator
Note that interest rate in % is used in the calculator  not in the equation.
Present Worth
Converts a uniform amount (annuity)  to a present value.
P = A [((1 + i)^{n}  1) / ( i (1 + i)^{n })] (5)
where
P = present value
A = amount per interest period
i = discount rate
n = discount periods
Download and print Present Value of Uniform Annuity chart
Example  Present Value of Uniform Amounts
The uniform amount (annuity) paid from a 7 years project is 5000. Calculate the present value with interest rate 5%.
The interest rate can be calculated
i = (5 %) / /100 %)
= 0.05
The present value of the uniform amounts can be calculated
P = 5000 [((1 + 0.05)^{7}  1) / ( 0.05 (1 + 0.05)^{7 })]
= 28932
Present Worth or Value  Online Calculator
Note that discount rate % is used in the calculator  not in the equation.
Capital Recovery
Converts a present value  to a uniform amount (annuity).
A = P [(i (1 + i)^{n}) / ((1+i)^{n}  1)] (6)
where
P = present value
A = amount per interest period
i = interest rate
n = discount periods
Download and print Capital Recovery  Uniform Annuity to Present Value
Capital Recovery  Online Calculator
Note that interest rate in % is used in the calculator  not in the equation.
Related Topics

Economics
Engineering economics  cash flow diagrams, present value, discount rates, internal rates of return  IRR, income taxes, inflation.
Related Documents

Cash Flow Diagrams
The future value of money. 
Compound Interest Tables
Compound interest tables  interests rates 0.25  60%. 
Interest Formulas
Future value of single cash flow. 
Interest Rate
Interest rate is the cost of money. 
Internal Rate of Return  IRR
Internal Rate of Return (IRR)  the breakeven interest rate. 
Net Present Worth (NPW) of a Cash Stream
The value of a stream of payments is called the Net Present Worth (NPW). 
Percentage
Working with relative values. 
Present Value
The value of money in the future is the Present Value.