Calculate Annual Rate of Growth

Here is the method to calculate the annual rate of growth over a period of time, e.g. salary or investment. In the following formula, the beginning balance is A, after Y years, the ending balance is B.

1. Calculate the percentage of change: B / A
2. Divide one by the number of years: 1 / Y
3. Calcualte the annul rate of growth: ( B / A ) ^ ( 1 / Y ) - 1
4. Convert the number in #3 to percentage

For example, the begining balance is 5000, after 10 year, the ending balance is 6000.

The annual rate of growth in 10 years is ( 6000 / 5000 ) ^ ( 1 / 10 ) – 1 = 0.0184 = 1.84%

Calculate After-Tax Mortgage Rate

Knowing the after-tax mortgage rate can help to determine whether prepaying the mortgage makes sense. Here is the formula.

After-tax mortgage rate = mortgage rate * ( 1 - federal income tax bracket )

To find your federal tax bracket, see this or this.

For example, the mortgage rate is 4%, the federal income tax bracket is 28%
the after-tax mortgage rate = 4% * ( 1 - 28% ) = 2.88%

The rate probably is lower, because you can also deduct the mortgage interest on your state income tax return.