# Interest Formulas

## Future value of single cash flow.

### Single Cash Accumulation - Future Value

The accumulated value of a present sum invested at a given interest rate after some time can be expressed as

F = P (1 + i)^{n}(1)

where

F = accumulated value in the future- Future Value

P = principal or present sum invested

i = interest rate per period

n = number of interest periods

The factor *"(1 + i) ^{n}"* is known as the "

*single payment compound amount factor*".

#### Example - Accumulated amount

An amount of *1000* is invested at interest rate *10% (0.1) per year* for *10 years*. The accumulated amount can be calculated like

F = 1000 (1 + 0.1)^{10}

= 2594

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#### Future Value Calculator

*Present Value*

* no. of periods*

* interest rate per period*

### Discounting Process - Present Value

The Present Value - or Present Worth - of a future cash flow can be calculated with the *discounting process* and is expressed like

P = F / (1 + i)^{n }(2)

where

P = present value

F = future cash flow

i = discount rate or discounting factor

n = numbers of periods

The factor *"1 / (1 + i) ^{n}"* is known as the "

*single payment present worth factor*".

#### Example - The present value of a future sum

A sum of *1000* is paid after *10 years*. The discount rate is *10% (0.1) per year*. The present value of the future payment can be calculated like

P = 1000 / (1 + 0.1)^{10}

= 386

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#### Present Value Calculator

*Present Value*

* no. of periods*

* interest rate per period*