Category Understanding the Mathematics of Personal Finance

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...

John Lennon once said, “Life is what happens to you while you’re busy making other plans.” Both taxation and inflation, it seems, are parts of life—they happen to you while you’re busy making other plans.

Taxation is the government’s way of getting money to pay its bills. You pay taxes on, among other things, your income; earned interest may be considered part of your income. The government (federal, state, and local) all want a piece of this income, so you get to keep and spend or save less than what all of the calculations thus far have promised you. On the other hand, interest on some of your debts is considered to be a deductible expense. That is, you get to reduce the income you report to the government, from which your tax burden is calculated, by this interest.

Inflation...

The pari-mutuel machine system used at race tracks offers a different approach to gambling. A roulette wheel owner is never sure what his or her daily operating cost will be; he or she only knows statistical generalities. On some nights, almost no one could win a lot of money; on some nights, there could be several lucky people. Also, the probabilities are fixed going into the game. The probability of the roulette wheel ball landing in any one slot is just 1/(number of slots) and the payoffs on any type of bet are published. The pari-mutuel machine system, on the other hand, adjusts the payoffs based on the bets, and the track owner can take a fixed amount or a percentage of the bets from each race. The easiest way to explain this is to work through an example.

Look at Table 14.1...

When you take a loan, the lender has legitimate up-front costs in preparing the paperwork, setting up the account, monitoring the payments, and so on. In the case of a mortgage, as shown in Chapter 4, the lender usually manages to charge you for these costs. In the case of an auto loan, there might not be any up-front costs. Instead, the lender estimates his or her costs and wraps them into the interest rate for the loan. This is equivalent to what I have shown at the end of Chapter 4; it’s just not shown explicitly—you’re quoted an interest rate and that’s that.

Suppose you were to acquire some money you didn’t think you’d have, or you have the savings, or for whatever reason you decide to pay the loan off early...

Another type of term life insurance is decreasing term life insurance. A decreasing term life insurance policy pays a little less each year for the term of the insurance. As an example, consider a $100,000, 20-year decreasing term policy. In year 1, the policy pays $100,000. In year 2, it pays $95,000 and so on, up to year 20, when it would pay $5,000.

At first blush, this seems like an odd sort of life insurance. Why would you want a beneficiary to receive less if you die later? This type of insurance is the equivalent of the loan insurance described in the last section, but it is more appropriate when it’s insuring a loan that is being paid off over time. If you are paying a loan back with regular payments, then each month you owe less...

Table 6.5 shows a month-by-month account of how things can go very, very, wrong. In doing the calculations, I’m just looking at monthly updates—I’ll assume that you