Understanding the Mathematics of Personal Finance

# 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. Assume that you have a savings account that earns 4% a year interest and you deposit \$1,000 into it at the beginning of the year. At the end of the year, you would have \$1,040 in your savings account and you should be able to buy more with this \$1,040 than you could have bought with your original \$1,000. If you left the money, at the end of the second year you would have \$1,081.60 (it should be obvious that I’m compounding annually), and you should be able to withdraw this money and buy even more if you so wished. If you want to buy bricks that cost \$1.00 each, when you had \$1,000 you could have bought 1,000 bricks. After the first year, you could have bought 1,040 bricks, or after the second year, you could have bought 1,082 bricks (rounding the numbers a bit).

Suppose that inflation is running at 6% a year. Starting with \$1,000, when bricks are \$1 each, you can buy 1,000 bricks. After the first year, you have \$1,040 in your bank account, but the same bricks now cost \$1.06 each. You can only buy 981 bricks. If you leave your money in the bank for 2 years, you have \$1,082, but bricks now cost \$1.12 each and you can only buy 966 bricks. Even though your bank account is growing, you are effectively getting poorer every year.

Inflation is particularly hard on people with fixed incomes, for example, retired pensioners. Each month, they receive the same check, and each month it’s worth less. The U. S. government provides periodic cost of living adjustments to social security payments to help counteract this problem. Go to http://www. ssa. gov/OACT/ COLA/latestCOLA. html to learn the specifics of this legislation.

Out of control inflation can destroy a country. Germany, after the first world war, had this problem; historians strongly correlate the high inflation rates to the demise of the Weimar Republic and to the rise of the Nazi party to power.

A low inflation rate that does not change abruptly is not difficult to live with. Savings bank interest rates tend to be higher than the inflation rate, so that actual savings and growth of buying power are possible.

Factoring the reality of inflation into long-term saving and borrowing is impor­tant. In the example I’m about to present, I’m using numbers that were chosen to be convenient for creating an example. I don’t know what the years will bring.

For this example, I’ll assume that inflation is a never-changing 4%. On January 1, 2000, I took a job that, after taxes, left me \$48,000 a year to live on. Using exist­ing savings for a down payment, I bought a home with a mortgage loan of \$2,000 a month, or \$24,000 a year, payments for 30 years. This might have been too much of a loan because my monthly mortgage loan payments eat up half of my available funds, but I am frugal and live within my means.

The company I work for is able to raise the price of its products to track with inflation; its costs also track with inflation, and even though I don’t advance much in my career, my salary also tracks with inflation. This means that in 2020, my available spending money, after taxes, is about \$105,000.[24] My grocery, gasoline, and so on costs also scale with inflation so it would appear that my standard of living has not changed.

One thing that did not scale with inflation is my monthly mortgage payment. I have a fixed rate, fixed payment, mortgage so I am still paying \$24,000 a year on my mortgage loan. But look what has changed: My mortgage loan payments used to be 50% of my after-tax earnings. In 2020, however, they are \$24,000/\$105,000 ~ 23% of my after-tax earnings. My standard of living certainly has changed—I now have more than 75% of my after-tax earnings to spend. I’m also well along the way to paying off my home, and if the next 10 years is like the first 20 years, it will get easier to make the payments every month.

Real situations are much more complicated than my simple examples.

To illustrate the impact of even modest inflation on planning for retirement (or any fixed income situation), I added an Inflation tab to the Ch9Taxation. xls spread­sheet. Hopefully, over the nest egg period, your salary was growing and you were able to periodically raise your contributions to your accounts. I’ll redo the retirement calculations with inflation to account for (Table 9.5).

Table 9.5 Retirement Phase of Nest Egg Building Example with Inflation

Input variables: Monthly withdrawal = \$750 Tax rate = 10%

Interest rate = 4.00%

Taxed savings Tax - deferred savings

 Mo Withdraw (\$) Balance (\$) Int (\$) Tax (\$) Mo Withdraw (\$) Balance (\$) Int (\$) Tax (\$) 1 750.00 83,382 278 28 1 750.00 127,782 426 75 2 751.25 82,881 276 28 2 751.25 127,382 425 75 3 752.50 82,377 275 27 3 752.50 126,979 423 75 4 753.76 81,870 273 27 4 753.76 126,574 422 75 5 755.01 81,361 271 27 5 755.01 126,166 421 75 6 756.27 80,849 269 27 6 756.27 125,755 419 75 7 757.53 80,334 268 27 7 757.53 125,342 418 75 8 758.79 79,816 266 27 8 758.79 124,926 416 75 9 760.06 79,295 264 26 9 760.06 124,507 415 75 119 912.85 2,182 7 1 119 912.85 59,507 198 75 120 914.38 1,275 4 0 120 914.38 58,716 196 75 121 915.90 363 1 0 121 915.90 57,921 193 75 122 917.43 -554 -2 0 122 917.43 57,122 190 75 123 918.96 56,318 188 75 124 920.49 55,511 185 75 180 1,010.46 3,019 10 75 181 1,012.14 1,942 6 75 182 1,013.83 859 3 75 183 1,015.52 - 228 - 1 75

Comparing Table 9.5 to Table 9.4, I have added a withdrawal column, which indexes the amount of money withdrawn up with inflation. I am assuming here that your cost of living will go up directly with inflation. This will not be the case if you have a fixed interest rate mortgage loan. In this case, only part of your expenses will go up with inflation. To correct for this, in the spreadsheet, just scale back the antici­pated rate of inflation to account for the fraction of your cost of living that will not grow with inflation.

Comparing the two tables, the savings bank account runs out of money 15 months earlier and the tax-deferred account runs out of money 17 months earlier due to inflation-indexed withdrawals. The tax-deferred account, with or without inflation issues, still outperforms the savings bank account.

PROBLEMS

1. Suppose that you and your significant other each have a taxable income of \$50,000 a year. The two of you could file your taxes as each being single, as being married filing jointly, or as being married filing separately (getting married is necessary for some of these choices, but I’m following the tax calculation thread here). Calculate your taxes in each situation. Is there a tax advantage to one of the situations?

2. Consider the same problem as above, but in this case, one of you has a taxable income of \$10,000 while the other has a taxable income of \$90,000.

3. This problem continues the study of Chapter 8, Comparing Loans. You have the choice of two competing mortgage loans, both for \$350,000. You can get a 6% APR 15-year loan or a 6.5% APR 20-year loan. The interest on these loans will be deductible from your taxes. This year your taxable income will be \$50,000. You have a very secure job, and you know that your taxable income will increase by 2% a year for the next 20 years, making the payments not an issue. Which loan is the better financial deal? Assume the loan is taken on January 1 and that the savings APR is 3.0%. Also, assume that the tax tables won’t change and that I can use the 2008 married filing jointly table.

4. When you retire, you want to spend \$40,000 a year from your savings to help support yourself. Inflation is running at 3% a year, however, and you notice that it costs you a little more each year to live the same way as you did the first year, so that you have to increase your initial \$40,000 withdrawal each year. If you start out with \$500,000 in your savings account, how many years will your money last? Assume that your savings are earning 5% interest a year.

5. You are (one of) a married couple filing jointly. Your taxable income this year will be about \$100,000. You have about \$25,000 to save or invest. Inflation is running at 2.5% annually. What APRs must you receive from a savings bank or from a tax-free investment to show an actual growth of 2% for the year? By actual growth, I mean growth in buying power.

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