Category Understanding the Mathematics of Personal Finance

LOANS WITH FIRST PAYMENT DUE IMMEDIATELY

When you borrow cash, you don’t usually make your first payment on the loan at the time you get your cash; instead, you wait for a month (or whatever the payment period is). When you never actually see the cash, for example, if you drive away in a financed new car, sometimes the first payment on the loan is due immediately rather than a month later.[11] Some online calculators let you take this variation into account.

The third tab in my spreadsheet, labeled Loan V2, calculates amortization tables for loans where the first payment is due at the date of the start of the loan.

In Table 3.8, I show (the first few lines of) a 15-year loan taken in May of 2008 for \$175,000 at an APR of 8.00% with the first payment due immediately...

DEDUCTIBLE INTEREST

The calculation of the amount of tax you don’t have to pay if you can deduct some interest is the same calculation as for the tax on taxable interest; you subtract the results from your taxable income rather than adding the results to it.

For example, suppose your taxable income is \$100,000, which (same tax table as above) would result in your owing approximately \$17,700 in taxes. If you have a sizeable loan such as a home mortgage, you might have paid \$10,000 in interest over the course of the year. If you can list this interest as a deduction, your taxable income drops to \$90,000 and your tax drops to approximately \$15,200. This is a saving of \$17,700 – \$15,200 = \$2,200 in tax.

Assuming that your loan is at 6% interest, we can approximate an effective interest rate by imagini...

Solutions

16.1 CHAPTER 1

1.

(a) 7 – (12 – 5) = 7 – 7 = 0

(b) 12(14 – 6) = 12(8) = 96

16-(3 + 7) _ 16-10 _ 6 _ 1 C 3 (7 – 5) _ 3 (2) _ 6 _

(d) (12 – 2)(7 + 3) = (10)(10) = 100

(e) 12 – 2(7 + 3) = 12 – 2(10) = 12 – 20 = -8

(f) (12 – 2)7 + 3 = (10)7 + 3 = 70 + 3 = 73

(g) 6.2 + 1/3 = 6.2 + 0.333 = 6.533 ~ 6.53

2.

(a) x + y + z = 6 + 2 + 3 = 9

(b) z(x – 3)(y + 2) = 3(6 – 3)(2 + 2) = 6(3)(4) = 72

x + 2 6 + 2 8

(c) + 2.25 _ -2-3 + 2.25 _ ^ + 2.25 _ — + 2.25 _ 8 + 2.25 _ 10.25

z – 4 3 – 4 -1 -1

(d) x(x – 1)(x + 2) = 6(6 – 1)(6 + 2) = 6(5)(8) = 240

3.

(a) T1 = 0 P3 = 0 N4 = 4 T5 = 8

Understanding the Mathematics of Personal Finance: An Introduction to Financial Literacy, by

Lawrence N. Dworsky

(b) At more than \$20 per wallet, £ Ni = 6 + 2 + 2 + 4 = 14.

6 i=1

All t...

Credit Cards

Credit cards are such an integral part of our society that it’s hard to imagine a time when they weren’t around. Store and gasoline credit cards have a long history, but the popularity of bank credit cards dates back only to the late 1960s. Today, it’s easy to get a card—either a bank, a store, or a gasoline card. Maybe it’s a little bit too easy to get a card; many people have several of them. It’s easy to make pur­chases; you just present the card. Electronic card readers collect your information and communicate with your credit card company almost instantly. Sometimes, it’s not so easy to fully pay for the purchases. And it’s incredibly easy to accrue balances on several different credit cards—balances that never seem to go away.

Gasoline and store credit cards are in...

BREAKING DOWN THE YEAR

This topic is a little math intensive and is not necessary for you to understand the rest of this chapter. The only sophisticated math, however, is handled using a spread­sheet function. If you’re willing to “go with” the use of the spreadsheet function and a brief explanation of what’ s happening, this section will give you a little more insight into the workings of Life Tables.

For whatever reason, an insurance company decided it would like to be able to sell term policies for half years rather than years. In order to price these policies, it

Table 10.6 Excerpt from the Life Table for Men with Some Curve Fitting Data

 Age q i Number of dead By fit % Error 45 0.003735 94,154 5,846 5,854 -0.14 46 0.004071 93,803 6,197 6,196 0.02 47

Present Value

Suppose you told me that you had

• walked into a television store,

• handed the store owner \$900, and

• walked out with a television that sold for \$1,000.

Assuming your story was true, I would conclude either that you were an amazing negotiator or that you were dealing with a very unintelligent (and soon to be out of business) store owner.

But what if your story was true (i. e., all the facts presented were absolutely correct), but something was omitted? Let’s retell the story with an omitted step: You

• walked into a television store,

• handed the store owner \$900,

• came back 2 years later, and

• walked out with a television that sold for \$1,000.

This is no longer an interesting story...