### !Compound Interest Calculations

Remember the compound interest model : P=Fx(1+i)-n and that:
• i is the interest or discount rate (decimal fraction) per accounting period.
• n is the number of accounting periods from 0, there may be several n's.
• P is a Present Value at time 0, may be positive or negative.
• F is a Future Value at a time n, may be positive or negative.
• A is a uniform amount per period for n periods, may be positive or negative.

#### The other compound interest model; P = qern assumes continous compounding

Calculators and computers have made many calculations easy. You can use an ordinary hand calculator, a very powerful computer, or anything in betweeen once you understand the concepts. You should also understand the behavior or the model, and the usual names of the variations in common use.

Unless you are using a printed copy of this note you have access to a PC, and the links below.

These NOTES include:
• Some Time ValueExamples including links to sample calculations by various tools.

• JavaScript versions of Time Value, Engineering Economy Compound Interest Functions
Note that you can do simple calculations in the data entry boxes of these functions.
The most common primitives and symbols are:
• multiplication *, e.g. changing years to months 6 * 12
• division /, e.g. changing a nominal annual rate to an effective short period rate such as 8.5% daily
would be 8.5 / 365
The JavaScript tools include a simple calculator that allows entry of one line algebraic expressions using JavaScript conventions.

• These notes use mostly Lotus 123, or EXCEL spread sheet examples. Note: Most spread sheet calculators have similar behaviors.

• A hand calculator which has a memory. Ideally the calculator should have yx, +/-, and 1/x keys. (specialized business analysis calculators with built in time value functions have been available for many years). If your calculator has an yx (X raised to power n) function it simplifies the calculations. The compound interest formulas are as shown on this link.

• J, a powerful concise computer language that is a descendent of APL ; J notes ; J interpreter
• APL - A long established high level computer language that has a mathematical ancestry.
Start demo APL workspace tv2 ; Note: Use 9 x 11 font size and expand the window for easy use.

Many text books about this and similar subjects contain tables of compound interest factors. Such tables are really not needed if a calculator with yx is available. The basis for the tables is versions of (1 + i)n.

A table of powers of (1 + i) is easily computed with an low level four function calculator. The table starts at time 0, then includes time 1, time 2, and so on until the number of periods is sufficient for your purposes. If your application is discounting, i.e. finding the present value of one or more future values make the table of the powers of 1 / (1 + i) n, i.e. (1+i)-n. If the application is estimating Future Values from present Values, then make the table of (1+i)n. For general use you can make a table that includes both powers of -n and n.