Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

This is an AMP page - Open full page! for all features.

• the most efficient way to navigate the Engineering ToolBox!

# 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

##### 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

##### 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

##### 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.

## Search Engineering ToolBox

• the most efficient way to navigate the Engineering ToolBox!

## SketchUp Extension - Online 3D modeling!

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp from the Sketchup Extension Warehouse!