Category Understanding the Mathematics of Personal Finance

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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Taxation and Inflation

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...

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DECREASING TERM INSURANCE

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...

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Prepayment Penalties

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...

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Investing: Risk versus Reward

If you kept all your savings in cash in a shoe box under your bed, you would be risking loss due to theft, fire, and so on. On the other hand, while your savings would never add up to anything other than exactly what you put into the shoe box, from a financial point of view, your savings would be absolutely safe. No stock market variations, bank failures, or whatever could impact your savings. Inflation, however, would slowly eat into the actual value of these savings, even though the dollar amount didn’t change.

Government-insured savings are, for all intents and purposes, perfectly safe. In addition, when your money is put into an insured saving product, you don’t have to worry about a burglar making off with it in the night...

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A BANKRUPTCY SPIRAL

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

Table 6.5 A Credit Card Disaster

Month

Balance ($)

Interest ($)

Tot Int ($)

Pmt

$200.00

0

254.50

2.00

2.00

Charge

$450.00

1

511.55

7.05

9.05

2

771.16

5.12

3

1,033.37

7.71

4

1,298.21

10.33

5

1,565.69

12.98

6

1,835.84

15.66

27

8,176.86

78.44

28

8,513.12

81.77

29

8,852.75

85.13

30

9,195.78

88.53

31

9,542.24

91.96

32

9,892.16

95.42

33

10,245.58

98.92

34

10,602.54

102.46

35

10,963.07

106.03

36

11,327.20

109.63

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