Explaining Compound Interest

Introduction

GnuCash offers the facility to do simple interest calculations for loans and interest-bearing deposits, giving you the ability to answer questions like "How long will it take me to pay off this loan?", "Which of these two term deposits generate better returns?", and "What loan payments do I need to make to pay off this loan in, say, five years?" GnuCash's financial calculator gives you that information, and more.

How Interest Works

There's two angles for talking about interest - interest-bearing accounts such as savings accounts and term deposits, when financial institutions pay you for the use of your money. Alternatively, we can discuss interest in the context of loans, where you pay your financial institution for using their money. To make things simple, we'll talk about loans first.

Firstly, let's consider the simplest possible loan where with a simple interest rate and we pay it back at the conclusion of the term. For example, let's say we borrow $10,000 (in financial terms, the Present Value is $10,000) for one year at an interest rate of 10% per annum that doesn't compound. How much do we owe at the end of it? In this case, calculating the Future Value that we owe is easy: it's just

	  Future Value = Present Value + (10 % * Present Value)
	               = 10,000 + (10% * 10,000)
	               = 11,000
	

Now, let's make things a bit more interesting. Let's make the interest compound monthly. After the first month, then, you'll owe

	  Future Value = 10,000 + (10% * 1/12)
	               ~= 10,083.33
	

Now, for the second month, you'll pay interest on the 10,083.83, so the value after the second month is:

	  Future Value = 10,083.83 + (10% * 1/12)
	              ~= 10167.36
	

Eventually, after 12 months, you'll owe $11,047.13, rather than the $11,000 you would have paid with simple interest.

Next, we'll make things more complex again - let's say we'll make a periodic payment of $200 at the end of every month? Well, let's see. After one month, you'd owe:

	  Future Value  = Present Value + Interest - Periodic Payment
          after month 1 = 10,000 + (10% * 1/12) - 200 
	                = 9,883.33
	

After one year, if you do the calculations, you'll still owe $8534.02 (if I've done my maths right . . .)

For our final example, consider continuous compounding, where interest is charged continuously. Explaining this calculation in detail requires a little bit of university-level maths, but, roughly, imagine that the payment periods are, really, really, really small! I can't easily show you the calculations for this, but that doesn't matter. GnuCash's financial calculator can do them!

So, to summarize, the following bits of information are used in interest calculations:

• Present Value

• Future Value

• Interest Rate

• Number of Payment Periods

• Periodic Payment

• Compounding Type (discrete or continuous)

• Compounding Interval (if discrete)

• Payment Time (beginning or end of period)