# 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.