## PAYING OFF A LOAN VERY SLOWLY

This section uses a little math, but I’ll go through it slowly in small steps. As with the previous section, this section is not necessary if you don’t want to tackle it.

I want to take a close look at what happens to the payment amount (S) as I take the same amount of loan, at the same interest rate, but for longer and longer times. In other words, I want to look at the payment formula above when I pick values for P, R, and У and leave them alone, but let n get larger and larger.

I’ll introduce the term r for the interest per payment period, just to make things a little neater. That is, let

R

r = —

У

so that I can write the payment formula as the much neater looking [10]

If n is very large, then (1 + r)n is much larger than 1, and (1 + r)n – 1 ~ (1 + r)n...

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