Understanding the Mathematics of Personal Finance

# DEFERRED TAXATION SAVINGS

The U. S. government offers several different tax deferral schemes for workers to use to build their “nest egg.” There are 401K plans, individual retirement accounts (IRAs), Roth IRAs, self-employed pension (SEP) IRAs, and so on. Each of these plans serves a different purpose/customer base, and each has its own rules about taxation, contribution, withdrawal, and so on. Many books have been written on this topic, and I couldn’t possibly do it justice in a few pages. What I will do in the fol­lowing pages is to walk through a hypothetical saving for a retirement example and show the potential value of a tax-deferred savings plan. I will be using my online spreadsheet Ch9Taxation. xls.

Г ’ rl begin using the Nest Egg tab on the spreadsheet. You are 40 years old, planning to retire at age 65. Your income puts you well into the 25% tax bracket.

Table 9.3 Nest Egg Building Example

Input variables: Nr Mnthly Pmts = 300 Interest rate = 4.00% Mnthly Pmt = \$250 Tax rate = 25%

Monthly contribution after withholding tax: \$188

 Pmt Nr Month Year Taxed savings Tax - deferred savings Balance (\$) Interest (\$) Tot Int/ Year (\$) Tax (\$) Balance (\$) Interest (\$) 1 1 1 188 0 0 250 0 2 2 1 376 1 1 501 1 3 3 1 564 1 2 753 2 4 4 1 754 2 4 1,005 3 5 5 1 944 3 6 1,258 3 6 6 1 1,134 3 9 1,513 4 7 7 1 1,326 4 13 1,768 5 8 8 1 1,518 4 18 2,023 6 9 9 1 1,710 5 23 2,280 7 10 10 1 1,903 6 28 2,538 8 11 11 1 2,097 6 35 2,796 8 12 12 1 2,281 7 42 10 3,056 9 13 1 2 2,476 8 8 3,316 10 14 2 2 2,672 8 16 3,577 11 15 3 2 2,869 9 25 3,839 12 296 8 25 82,737 274 2,151 125,841 417 297 9 25 83,201 276 2,427 126,511 419 298 10 25 83,666 277 2,704 127,182 422 299 11 25 84,132 279 2,983 127,856 424 300 12 25 83,784 280 3,264 816 128,532 426

You want to divert \$250 of your gross salary each month to an account that will give you 4% interest annual percentage rate (APR). This example is shown in Table 9.3 .

The first thing that happens is that some money is withheld from your paycheck for taxes. To keep things simple, I’ll assume that the exact tax payment is deducted each month. I’m ignoring social security, Medicare, state tax, and any other deduc­tions. The money you have available to contribute is 75% of \$250 = \$188 (cell K1 on the spreadsheet). The spreadsheet shows the balance growth each month and the interest paid into the account each month. At the end of the year, tax is paid on the year’s interest, and this amount is deducted from the balance.1

At the end of 25 years (300 monthly payments), your balance, after taxes, is \$83,784.

Look at the tax-deferred savings columns. Assuming your plan deposits pay­ments pretax (some, but not all of them do), the full \$250 goes into the account every month. The interest accrued does not get taxed, and at the end of the 25-year period, the balance in the account is \$128,532.

The tax-deferred plan has about 50% more in it than the simple savings plan. Remember, however, that the simple savings plan money is all yours at this

Table 9.4 Retirement Phase of Nest Egg Building Example

 Input variables: Monthly withdrawal = Tax rate = 10% Interest rate = 4.00% \$750 Taxed savings Tax - deferred savings Month Balance Interest Tax Month Balance Interest Tax (\$) (\$) (\$) (\$) (\$) (\$) 1 83,382 278 28 1 127,782 426 75 2 82,882 276 28 2 127,383 425 75 3 82,381 275 27 3 126,983 423 75 4 81,878 273 27 4 126,581 422 75 5 81,374 271 27 5 126,178 421 75 6 80,868 270 27 6 125,774 419 75 7 80,360 268 27 7 125,368 418 75 8 79,851 266 27 8 124,961 417 75 9 79,341 264 26 9 124,552 415 75 134 1,832 6 1 134 61,130 204 75 135 1,087 4 0 135 60,509 202 75 136 341 1 0 136 59,886 200 75 137 -408 - 1 0 137 59,260 198 75 138 58,633 195 75 139 58,003 193 75 217 1,842 6 75 218 1,024 3 75 219 202 1 75 220 - 622 -2 75

1 If I were doing present value calculations, I’d note that the tax on the year’s interest doesn’t get paid until the following April. For these examples, I’m keeping things simple by just deducting the tax payment from the balance at the end of the year.

point—it’s all after-tax money. The money in the deferred tax plan is still yet to be paid.

Now look at the Retirement tab of Ch9Taxation. xls (shown in Table 9.4). I’ve simplified the calculations in that I show the tax generated each month being paid that month. Let’s say you would like to draw \$750 each month from your account. Since you’re retired, you’re probably in a lower tax bracket than you were when you were working. I’ll use 10% for the example. I left the interest rate at 4%; this of course could have changed over the years.

In the case of the taxed savings account, the tax is the tax rate multiplied by the interest earned (each month). For this tax-deferred plan, you pay taxes on the money as you withdraw it. The taxed savings monthly tax starts off lower than the tax-deferred savings monthly tax and gets a little lower every month. The higher initial balance in the tax-deferred savings account outweighs this tax disadvantage, however: The taxed savings account runs out of money in about ІШ years, while the tax-deferred account lasts about 18^ years. This is significantly a better retirement funding.

A word of warning: Each government - approved plan has its own rules about taxing contributions and taxing disbursements. There are also rules about withdrawing money from the account while still in the “nest egg” phase, as well as rules about maximum contributions, and rules about everything else (there are probably rules about writing rules). To make it worse, these rules keep changing. Do your homework.

In good times, many employers will match employees’ contributions to retire­ment funds up to some maximum percentage specified by the IRS. This is an effec­tive pay raise. If you find yourself in this fortunate situation, increase the nest egg contribution amount in the spreadsheet by your employer’s contribution to see how your balance will grow. Keep in mind that this contribution only applies to the tax - deferred savings numbers; there is no matching contribution for a personal savings account.

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