# Category Understanding the Mathematics of Personal Finance

## 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...

## SHORT SALES

So far, this chapter presumed that the way to make money is to “buy low, sell high.” This is true, but it isn’t the only way to make money. Buying a stock in the hope that its price will rise is called “going long.” Conversely, if you think a stock’s price will fall, you can “go short” or “sell short.” The way to do this is to arrange to borrow some stock that is selling at, say, \$25 a share, and selling it. When the price falls to \$20 a share you buy back the stock, return the shares and any costs for the loan, and keep the difference. If the stock price goes up instead of down, you’ll have to pay more than you received when you sold the stock, and you’ll lose money on the transaction.

13.4 STOCK DIVIDENDS

Corporations may declare dividends...