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Interest Rate

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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

Accumulated Value Year by Year with Interest Rate 10%
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.


Download and print Future Value of Present Payment chart

Interest Rate - Online Calculator


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 %

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Related Topics

Economics

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

Related Documents

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The future value of money.

Compound Interest Tables

Compound interest tables - interests rates 0.25 - 60%.

Contract Types

Commonly used engineering and construction contracts.

Discrete Compounding Cash Flow Formulas

Discrete payments compounding equations and online calculators .

Interest Formulas

Future value of single cash flow.

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).

Present Value

The value of money in the future is the Present Value.

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