Understanding the Mathematics of Personal Finance


While determining what interest is taxable and what interest isn’t taxable can be a fairly sophisticated task, figuring out the tax on taxable interest is very straightfor­ward. Let’s say that your taxable income is $50,000 not counting interest. Your tax is approximately $6,700, which is an average tax rate of 13% and an incremental tax rate of 15%. If you have $10,000 of savings earning 4% interest, you earned $400 in interest last year. This interest is taxed at the 15% rate, so the tax on your interest is 0.15(400) = $60.

If your interest was $400 but you had to send $60 back to the government, then you only got to keep $400 - $60 = $340. Your effective interest rate was therefore

$340 $10,000 = 3.4%.

If your taxable income, not counting interest, had been $360,000, your tax would have been approximately $97,600. This is an average tax rate of 27% and an incre­mental tax rate of 35%. Now, the tax on the $400 interest is 0.35(400) = $140, and you get to keep only $260 of the $400. Your effective interest rate on your earnings is

$260 $10,000 = 2.6%.

Remember that the tax on your earnings excluding this interest does not go up because of the interest earnings. It remains exactly the same.

Some very secure investments are “tax free.” This means that you do not pay taxes on the interest from these investments. This tax-free status might apply to the federal tax, the state tax, or both—research this point carefully. If one of these investments paid 3% interest when you could get 4% interest on a certificate of deposit, you might first head toward the certificate of deposit. If you are in a high enough tax bracket that the effective interest rate on the certificate of deposit is lower
than 3%, as it is in the above example, then the tax-free investment suddenly starts to make sense.

Calculating the tax and the effective interest rate on an investment gets a little bit more complicated if your taxable income is very close to (but less than) the upper edge of a tax bracket.

For example, suppose your taxable income was $130,000 and you earned $3,000 in interest last year; staying with the married filing jointly table, note that the tax bracket jumps from 15% to 25% at a taxable income of $131,450. Therefore, $1,450 of your interest gets taxed at 25% and the remaining $1,550 gets taxed at 28%:

Tax = 0.25 ($1,450) + 0.28 ($1,550) = $362.50 + $434.00 = $796.50.

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