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# Interest Rate

## Interest rate is the cost of money.

Interest is the cost of money and is measured by the interest rate where

interest rate = cost of having money available for use

The interest rate is a percentage that is periodically added to an amount of money over a specified length of time. If money is borrowed the interest rate is the percentage of the borrowed amount that is paid to the borrower as a compensation for the use of the borrowed property.

Interest reflects that

• money available today has a greater value that money received in the future

The future value of a present amount of value can be expressed as

F = P (1 + i)n                     (1)

where

F = future value

P = present value

i = interest rate per period

n = number of interest periods

### Example - Accumulated Value

The accumulated value of an amount of present value 1 today with interest rate 10% in a 10 years period can be expressed as

YearAccumulated Value
0 1
1 1.1
2 1.21
3 1.33
4 1.46
5 1.61
6 1.77
7 1.94
8 2.14
9 2.36
10 2.59

An amount of 500 will accumulate with the factor 2.14 in 8 years - or

F = 2.14 (500)

= 1070

### Future Value of Present Money due to Interest Rate - Calculator Table

This calculated table visualizes the increase in future value of present money due to interest rate and time.

Present Value of Money

Start Year

End Year

Max. Interest Rate (%)

### Interest Rate - Online Calculator

P - Present value

i - interest rate per period (%)

n - number of periods

### Finding Unknown Interest Rate

If a single payment P shall produce a future value F after n annual compounding periods, the per annum decimal interest rate can be calculated as

i = (F / P)1/n - 1                              (2)

#### Example - Finding Interest Rate

A single payment of 100 today shall grow to 120 in 5 years. The required interest rate can be calculated as

i = (120 / 100)1/5 - 1

= 0.037

= 3.7 %

## Related Topics

• Economics - Engineering economics - cash flow diagrams, present value, discount rates, internal rates of return - IRR, income taxes, inflation.

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