Discrete Compounding Cash Flow Formulas
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
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
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 break-even 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.