Math Formulas

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 Part, over Base times Rate; also called Result, over Base times Rate; also called the “Pie Formula” or the “T Formula” (It’s all the same thing), can be used in a variety of circumstances.  If you know any two of the three pieces in the formula, you can figure out the one you’re missing.  For example, in Commission problems (shown at the right), the Sale Price times the Commission Rate would give you the Commission (the actual dollar amount paid by the seller.  The Commission divided by the Commission Rate would give you the Sale Price, and the Commission divided by the Sale Price would give you the rate in decimals (you then need to move the decimal point two places to the right to convert it to a percentage). For Commission problems, the formula would be:   _______Commission________ Sale Price X Commission Rate   To figure the share received by a salesperson or by another broker use:   Salesperson’s or Other Broker’s Share      Total Commission X Percentage   To figure the amount received by the seller after paying the commission use:   ____________Seller’s Net____________ Sale Price X (100% – Commission Rate) For Tax problems, the formula would be:   _______Annual Tax_______ Assessed Value X Tax Rate   Remember the rate will be expressed in Mills (1 Mill = .001, 50 mills would be .050, and so on).   To find the Assessed Value from the Market Value (or vice-versa):   ________Assessed Value_______ Market Value X Assessment (Rate)   If you are prorating taxes (or anything else) between a buyer and a seller, make sure you know whether your state exam uses a 360-day year or a 365-day year.  That will affect your answer.  Also make sure you know who is responsible for the day of settlement and when taxes are considered to be due on the state exam. For Interest Problems:   _______Interest_______ Principal X Interest Rate   Remember, the Principal is the CURRENT balance of the loan.  Also remember, the time period for the Interest and the Interest Rate MUST be the same.  Interest Rates are normally quoted at a yearly rate, which would mean you would normally get a year’s worth of interest up top.  If you needed the monthly interest you would divide by 12.  If you knew the monthly interest, you would first multiply by 12, so you could insert the yearly amount into the formula.  If you have the interest for a different time period (such as quarterly or for multiple years), then pay careful attention, so you are converting to a yearly amount. To Calculate Profit or Return:   ____Amount of Profit or Return_____ Original Investment X Rate of Return   Rate of Return also would probably be calculated on an annual basis, unless the question asks for the TOTAL Return.  Percentage of Profit probably would be the total amount, unless the question asks for the annual amount. Just a quick review of factor charts, which are used to calculate the monthly payment for principal and interest on a Fully Amortized Loan.   Using the chart to the right as an example, start in the left column and find the interest rate.  Next, go across until you are under the term of the loan.  That number would be the factor.  For example, if you go down to 8%, and across to 30 years will give you a factor of 7.34.   Once you have the factor, multiply that number by the number of thousands in the loan (the loan amount divided by 1000).  A 100,000 dollar loan divided by 1000 would equal 100.  That multiplied by a factor of 7.34, would give you a monthly payment of \$734 for principal and interest. Rate/Term     15-year          30-year     7%                  8.98               6.65   7˝%               9.27               6.99   8%                  9.56               7.34   8˝%               9.85               7.69               Did I forget anything?