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Discrete Compounding Formulas

Compounding formulas for discrete payments

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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

single payment present amount diagram

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

single payment compound amount diagram

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

uniform series compound amount diagram

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

uniform series sinking fund diagram

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

uniform series present wort value diagram

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

uniform series capital recovery diagram

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.

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