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# Discrete Compounding Formulas

## Compounding formulas for discrete payments

### 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

P - single payment today

i - interest (%)

n - number of periods

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

F - single future payment

i - discount rate (%)

n - number of periods

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

A - uniform amount per period

i - interest rate (%)

n - number of periods

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

F - future value

i - interest rate (%)

n - number of periods

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

A - uniform amount per interest period

i - discount rate (%)

n - number of periods

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

P - present value

i - interest rate (%)

n - number of periods

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

## Tag Search

• en: engineering economics discounting annuity interest rate cash flow compound payments

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## Citation

• Engineering ToolBox, (2008). Discrete Compounding Formulas. [online] Available at: https://www.engineeringtoolbox.com/discrete-payments-compounding-formulas-d_1234.html [Accessed Day Mo. Year].

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