Category Understanding the Mathematics of Personal Finance

THE EFFECT OF INTEREST RATES ON PRESENT VALUE CALCULATIONS

The present value of amounts of money in the future, as the above calculations show, depends on the available interest rate. If interest rates are very low, then the present value looks essentially like the simple sum of all the payments. As interest rates get higher, payments far in the future become pretty worthless.

Table 7.3 shows the total present value of a 24 monthly payment account with $100 being deposited each month for different interest rates. As you can see from the table, the present value falls as the rate of interest increases.

One factor that’s very easy to model on a spreadsheet but very difficult to predict in advance is just what interest rates will be a few years from now...

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OPTIONS

Many types of “futures” products are available for the aggressive investor. I’m going to explain just one of them: options. A stock option gives the purchaser the right, but not the obligation, to buy (a “call”) or to sell (a “put”) a certain number of shares of a given stock for a preset price at any time up until the expiration date of the option.

That was a mouthful. Let me break it down, using the option to buy, or call, for an example. Widgetarama stock is selling at $28 (per sharei ) and I believe it will increase significantly in price over the next 90 days. I find that I can buy calls on Widgetarama stock for $4.00 with a strike price of $26 and an expiration date of 90 days from now...

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REGULAR SAVINGS

The other side of making regular payments to amortize a loan is making regular payments into a savings account so as to build up resources for your retirement, for a child’s college education, and so on.

Suppose you could start saving $350 a month regularly. Savings bank interest rates will probably vary, but just to get an idea of what will happen, assume that they

Table 3.10 A Savings Plan Spreadsheet Example

Start Month:

7

Start Year:

2005

Nr Mnthly Pmts

360

Rate

4.50%

Monthly Pmt

$350.00

Pmt Nr

Mnth

Year

Balance ($)

Payment ($)

Interest ($)

Tot Int/Year ($)

1

7

2005

350.00

350.00

0.00

0.00

2

8

2005

701.31

350.00

1.31

1.31

3

9

2005

1,053.94

350.00

2.63

3.94

4

10

2005

1,407.89

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ONLINE DEFERRED TAXATION PLAN CALCULATORS

This site calculates how a 401K savings plan benefits you: http://www. bloomberg. com/invest/calculators/401k. html.

The bloomberg. com host site is a treasure trove of financial calculators: http:// www. bloomberg. com/invest/calculators/index. html.

This site isn’- a calculator. It’s a U. S. government (Department of Labor) site about 401K plan fees: http://www. dol. gov/ebsa/publications/401k_employee. html.

9.3 INFLATION

When you pay taxes or get a tax deduction, you can see the actual dollar amounts coming and/or going, relate this to expenditures and income, and plan your financial activities accordingly. Inflation is different. Inflation is a devaluation of the buying power of a dollar...

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TRANSFERS

Transfers are “deals” offered by a credit card company to lure you away from another credit card company. Each offered deal is unique, so you might have to do a little work to evaluate, compare, and contrast them.

Let me create a fictional transfer deal: If you transfer your balance from credit card company X to credit card company Y, company Y will allow you to maintain that balance, and possibly some level of new purchases, for 12 months (from the transfer date) at 0% interest. This can be a very good offer. Remember that there is always a time value of money, so an offer to assume a debt of yours (your outstand­ing balance at company X) for a year with no interest is in effect paying you to switch credit card companies.

Just how much this deal is worth depends on what your balance ...

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A BENCHMARK SAVINGS PLAN

In order to understand the advantages (and possible pitfalls) of a fixed annuity, it’s useful to compare the annuity to a personal savings plan. The spreadsheet on my website Ch11FixedAnnuities. xls will help with these calculations. Go to the IAWPC tab (I ’ Il explain this mysterious acronym soon). This example is shown in Table 11.1 .

In this spreadsheet, I chose a starting month as month #1 so that the month number and the number of months gone by would be the same. The spreadsheet fixes the starting year at 1; I did this because we we’re looking at years into the plan rather than actual dates.

I want to receive a payment of $2,500 each month, for 20 years, from this account. The annual percentage rate (APR) is 4.0%. My tax rate is 25%.

The calculated principal is $413,930 (top of...

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