Understanding the Mathematics of Personal Finance

# IMMEDIATE ANNUITY WITH PERIOD CERTAIN

An immediate annuity is an annuity that starts making payments immediately. Period certain means that we’re specifying how often the payments are made and how many payments there will be. This is the IAWPC acronym on the spreadsheet tab.

Once again, I am pointing out that anything I say about taxes might not be true when you’re reading it. Tax laws change.

Assuming that things don’t change drastically, the attraction of an annuity lies in how it is taxed. You pay taxes only on the money you pull out of the annuity (the

Table 11.1a Example of an IAWPC as Compared with a Savings Account

Nr monthly payments: 240

 Payment: Rate: Tax rate: \$2,500 4% 25% Savings: Pmt Nr Calculated principal: \$413,929.83 PV of tax bills: \$37,322 Mnth Year Balance Interest Tax Tax bill PV (\$) (\$) 1 1 1 411,429.83 0.00 0.00 2 2 1 410,301.26 1 ,371.43 342.86 3 3 1 409,168.93 1 ,367.67 341.92 4 4 1 408,032.83 1 ,363.90 340.97 5 5 1 406,892.94 1 ,360.11 340.03 6 6 1 405,749.25 1 ,356.31 339.08 7 7 1 404,601.74 1 ,352.50 338.12 8 8 1 403,450.42 1 ,348.67 337.17 9 9 1 402,295.25 1 ,344.83 336.21 10 10 1 401,136.24 1 ,340.98 335.25 11 11 1 399,973.36 1 ,337.12 334.28 12 12 1 398,806.60 1 ,333.24 333.31 13 1 2 397,635.96 1 ,329.36 332.34 14 2 2 396,461.41 1 ,325.45 331.36 15 3 2 395,282.95 1 ,321.54 330.38 16 4 2 394,100.56 1 ,317.61 329.40 4,051.53 3,854.26 17 5 2 392,914.23 1 ,313.67 328.42 18 6 2 391,723.94 1 ,309.71 327.43 19 7 2 390,529.69 1 ,305.75 326.44 237 9 20 7,450.28 33.06 8.26 238 10 20 4,975.11 24.83 6.21 239 11 20 2,491.69 16.58 4.15 240 12 20 0.00 8.31 2.08 160.00 71.27

Table 11.1b Example of an IAWPC as Compared with a Savings Account

Nr monthly payments: 240

Payment: \$2,500

Rate: 4%

Tax rate: 25%

Annuity:

 Pmt Nr Exclusion ratio: 0.690 PV: \$33,596 Mnth Year Taxable (\$) Tax (\$) Tax bill (\$) PV (\$) 1 1 1 775.29 193.82 2 2 1 775.29 193.82 3 3 1 775.29 193.82 4 4 1 775.29 193.82 5 5 1 775.29 193.82 6 6 1 775.29 193.82 7 7 1 775.29 193.82 8 8 1 775.29 193.82 9 9 1 775.29 193.82 10 10 1 775.29 193.82 11 11 1 775.29 193.82 12 12 1 775.29 193.82 13 1 2 775.29 193.82 14 2 2 775.29 193.82 15 3 2 775.29 193.82 16 4 2 775.29 193.82 2,519.70 2,397.01 17 5 2 775.29 193.82 18 6 2 775.29 193.82 19 7 2 775.29 193.82 237 9 20 775.29 193.82 238 10 20 775.29 193.82 239 11 20 775.29 193.82 240 12 20 775.29 193.82 2,325.88 1,036.08

Since insurance companies sell these plans, you may see the principal referred to as the premium. The denominator is the sum of all the payments. For this example,

The fraction of each payment that’s taxed is 1 - 0.690 = 0.31. Given that all the payments are the same, all the tax bills are the same, as shown in columns N through O. In column Q, I showed the present value of these payments, and at the top of the column, I showed the sum of these present values (\$33,596).

The present value of the tax bill for the annuity is definitely lower than the present value of the tax bill for the savings account. In addition, examining the tax payments shows that the savings account tax bills are “front loaded”—they are large in early years and small in later years. The tax payments of the annuity are the same year to year. In an economy where there is always some level of inflation, this means that a larger fraction of the annuity tax bills than of the savings tax bills is paid for with “cheaper” dollars. This can be a good thing for you, as was explained in Chapter 9 .

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