Compound Interest Formula Explanation and Analysis

Here we will look at the compound interest formula.  This formula is extremely useful in investment calculations, and in calculations of offer prices for various types of cash flows.

Compound Interest Formula Explanation

Shown here in figure 1 is the compound interest formula.

P = Principal amount
r = annual rate of interest; for example 10% would be 0.1
t = number of years
A = Amount of money after n years has elapsed
n = number of times the interest is compounded per year

Now, if n happens to be 1, as in interest compounded once per year (also known as rate per annum, or rate p.a.), then the formula simplifies to A = P(1+r)^t

A common use of this compound interest formula is to calculate how much money would be worth if kept in a savings account in a bank.  For example, $100 earning 1% per annum for 10 years would be worth $110.46.

A = P(1+r)^t  = $100(1+.01)¹⁰ = $100(1.01¹⁰) = $100(1.1046) = $110.46

But now let's make this compound interest calculation a little more interesting - and useful for making money.

Solving the Compound Interest Formula for Principal

How about we solve this compound interest equation for P.  Then, we could pick a rate of return we would like to achieve.  Then for any opportunity where we know the value of an item at a given point in time (let's call it the maturity date), we could calculate how much that opportunity is worth in advance of the maturity date.

So to get to it, solving for P gives us the following equation shown in figure 2:

Now we're getting somewhere.  Now we can use this formula in evaluating cash flow opportunities.

The compound interest formulas in Microsoft Word 2007 format are available here: Compound-Interest-Formula-Explained-1.docx

If you have questions, please post a comment below, or visit the forum.