# ONLINE CALCULATORS

I found so many excellent compound interest calculators that I’ m only listing a representative sample. All of the calculators I found have a good graphical interface. Most of them want the interest rate stated as a percentage, that is, 10%, not 0.1. Some of them let you invert the problem arbitrarily. That is, you can pick any three of the four variables’ future value, principal, years, and rate, and the calculator will solve for the fourth variable. Future value in the examples above is the balance at the end of the loan:

2.1 SCALING

This section is not necessary for understanding and working with the rest of the book. Its conclusion, however, is very easy to understand, so glance at it even if you’re uncomfortable with the math.

Looking at the formula for loan balance above, we see that there are four numbers necessary to calculate a balance: P, R, y, and n. Suppose we have done all
our calculations and we want to know what happens if we were to borrow \$10,000 instead of \$5,000. In other words, we’re doubling P.

For those of you comfortable with the algebra,    (2P )[l + R

where b was the original balance.

What this is saying is that if I’ve calculated a balance for some numbers P, R, y, and n and then I double P (the principal), the balance doubles. If I were to divide the principal by a factor of 3, the balance would divide by a factor of 3. This property is called “linear scaling of the balance with respect to the principal.”

Let’s look at this situation without the algebra. If my friend and I open identical savings accounts and put in the same amount of money, at any time in the future we would expect our balances to also be identical. This means that starting with twice the principal must lead to twice the balance at any time.

This property of linear scaling only holds for the principal; if I change R, y, and/ or n, the balance certainly will change, but there’s no way to predict the change other than by actually doing the calculation.