Unit F: Finance

Determining the Monthly Payments and Number of Payments


When discussing the options available for a loan to start a small business, financial institutions use spreadsheets and computer programs to calculate the monthly payment of a loan or the number of payments required to pay back a loan.

The borrower is given many options that must be evaluated with regard to how long and how much the payments are, the feasibility for the business to afford payments each month or year, and the amount of interest paid during the life of the loan.

Aaron would like to make a monthly payment of $400.00 for the start-up loan of $13 700.00. Using the Number of Monthly Payment Calculator, determine the length of time in years that it will take for Aaron to pay off the loan, if the interest rate is 4.5%.




Use the Number of Monthly Payments Calculator to find the number of payments. Record the information in a chart.

principal 13 700.00
annual interest rate
 4.5%
monthly payment
 400
number of monthly payments
 37

Aaron would have 37 monthly payments.

To find the length of time to pay off the loan, convert 37 months to years.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»37«/mn»«mo»§#160;«/mo»«mi»months«/mi»«mo»§#215;«/mo»«mfrac»«mrow»«mn»1«/mn»«mo»§#160;«/mo»«mi»year«/mi»«/mrow»«mrow»«mn»12«/mn»«mo»§#160;«/mo»«mi»months«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mn»3«/mn»«mo».«/mo»«mn»08«/mn»«mo»§#160;«/mo»«mi»years«/mi»«/math»

It would take Aaron 3.08 years to pay off the loan.
Aaron plans to pay the start-up loan back over a 10-year period.

  1. What would his monthly payment be if the interest rate is 4.5%?


  2. Calculate the total amount that Aaron pays for the loan.
  3. Calculate the amount of interest that Aaron pays to the bank.

  1. Convert 10 years to months.

    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»10«/mn»«mo»§#160;«/mo»«mi»years«/mi»«mo»§#215;«/mo»«mfrac»«mrow»«mn»12«/mn»«mo»§#160;«/mo»«mi»months«/mi»«/mrow»«mrow»«mn»1«/mn»«mo»§#160;«/mo»«mi»year«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mn»120«/mn»«mo»§#160;«/mo»«mi»months«/mi»«/math»

    Use the Monthly Payment Calculator to find the monthly payment. Record the information in a chart.

    principal 13 700.00
    annual interest rate
    		 4.5%
    number of monthly payments
    		 120
    monthly payment amount
    		 141.98

    The monthly payment is $141.98 on the 10-year loan.

  2. To find the total amount Aaron pays for the loan, multiply the monthly payment by the number of monthly payments. The total amount that Aaron pays is

    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«mi»total«/mi»«mo»§#160;«/mo»«mi»cost«/mi»«mo»§#160;«/mo»«mi»of«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»a«/mi»«mo»§#160;«/mo»«mi»loan«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»montly«/mi»«mo»§#160;«/mo»«mi»payment«/mi»«mo»§#215;«/mo»«mi»number«/mi»«mo»§#160;«/mo»«mi»of«/mi»«mo»§#160;«/mo»«mi»monthly«/mi»«mo»§#160;«/mo»«mi»payments«/mi»«/mtd»«/mtr»«mtr»«mtd»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»$«/mo»«mn»141«/mn»«mo».«/mo»«mn»98«/mn»«mo»/«/mo»«mi»month«/mi»«mo»§#215;«/mo»«mn»120«/mn»«mo»§#160;«/mo»«mi»months«/mi»«/mtd»«/mtr»«mtr»«mtd»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»$«/mo»«mn»17«/mn»«mo»§#160;«/mo»«mn»037«/mn»«mo».«/mo»«mn»60«/mn»«/mtd»«/mtr»«/mtable»«/math»

    Aaron pays a total of $17 037.60 for his loan.

  3. In a loan, the interest is the amount of money paid above the original amount of the loan.

    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«mi»interest«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»total«/mi»«mo»§#160;«/mo»«mi»amount«/mi»«mo»§#160;«/mo»«mi»paid«/mi»«mo»§#160;«/mo»«mi»to«/mi»«mo»§#160;«/mo»«mi»bank«/mi»«mo»-«/mo»«mi»initial«/mi»«mo»§#160;«/mo»«mi»amount«/mi»«mo»§#160;«/mo»«mi»of«/mi»«mo»§#160;«/mo»«mi»loan«/mi»«/mtd»«/mtr»«mtr»«mtd»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»$«/mo»«mn»17«/mn»«mo»§#160;«/mo»«mn»037«/mn»«mo».«/mo»«mn»60«/mn»«mo»-«/mo»«mo»$«/mo»«mn»13«/mn»«mo»§#160;«/mo»«mn»700«/mn»«mo».«/mo»«mn»00«/mn»«/mtd»«/mtr»«mtr»«mtd»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»$«/mo»«mn»3«/mn»«mo»§#160;«/mo»«mn»337«/mn»«mo».«/mo»«mn»60«/mn»«/mtd»«/mtr»«/mtable»«/math»

    Aaron paid $3 337.60 in interest to the bank for the loan.