In addition to tax filing season, April is Mathematics Awareness Month. This is a great time to review some useful math tricks to improve your short-term budget and long-term financial plans.
It is important to remember that the following equations are simple estimations and are not to be treated as precise technical calculations. Each equation can be influenced by a number of factors and do not take your personal financial situation into account. The formulas are meant to provide a rough estimate, not an exact projection.
Income – expenses = surplus or deficit
This is the easiest place to start. By subtracting all planned expenses from gross income, you find the total surplus or deficit you have each month. If you find you are running a deficit most months, you need to cut your expenses down, find a way to boost your income, or some combination of the two.
Cost x 12 = annual expense
Another easy formula is how to calculate the cost of a monthly expense over a whole year; this is an important insight for any budget. Paying $8 a month for a subscription may seem cheap, but you may reconsider if you realize it is costing you $96 over the course of a year.
Cost of 1 gallon of gas x 500 = annual gas expense
The EPA estimates that the average car owner uses about 500 gallons of gas a year
(but can be as much as 700 if you drive a truck or SUV). Volatile gas prices make it impossible to project your exact gas expenses for a year. This formula, however, makes it easy to understand the effects of a fluctuation in gas price: For every cent devaluation of gas, you could expect to save $5 annually.
72 / percent of return = years to double
Have you ever wanted a quick estimate of how long it takes for money to double? Try the “Rule of 72.” Just divide 72 by the annual growth rate of your account, and you get an approximation of how many years it takes to double.
(Example: Six percent growth would be 72/6 = 12 years to double).
If using this formula for an investment account, remember that the market is unpredictable and average market performance does not guarantee future returns. Investments can be subject to losses, which will significantly change their nominal rate of return.
(Years of ownership + 1) x .10 = car depreciation percentage
Although there are some major outliers, most new cars depreciate around 10 percent when driven off the lot and another 10 percent each year they are driven (for the first five years). So when looking at new cars, remember that most lose their value fast. Without a down payment, you will likely be underwater on the loan for the first year or two.
Mortgage x (.03+(Rate x .75)) = annual mortgage cost
This equation is a bit more complex, but it is pretty handy for people wondering how their rent cost compares to a 30-year mortgage. Take 75 percent of the expected mortgage interest rate and add 3 percent to get the annualized rate of repayment. If you multiply this number by the initial mortgage amount, you get the annual cost.
For example: A 30-year mortgage issued at 4 percent would have an annual repayment rate of .03+(.04×.75) = 6 percent. If the mortgage was for $200,000, you would pay ($200,000×6 percent)= $12,000 per year (or $1,000 a month) to stay on the 30-year schedule.
Keep in mind that this is an estimation of the mortgage costs only and does not include home insurance, mortgage insurance, property expenses, or any of the other various costs of owning a home.
