MA.912.FL.3.6

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

• MA.912.FL.1

Terms from the K-12 Glossary

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• MA.912.FL.3.4

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Purpose and Instructional Strategies

• Instruction of this benchmark includes how APR and periodic rate are calculated per month and the connection between the two percentages. Students should also have an understanding of common financial terms. 
• For loans and installment plans, the key to finding the finance charge is calculating the total paid over the term of the loan or plan and then subtracting the amount of the purchase. To find the total amount paid, students should use the formula below to calculate the monthly payment for the loan or installment plan and then multiply this amount by the number of months of the loan or installment plan. 

• For example, Sasha is buying her first home and plans to take out a 30-year, $235,000 mortgage with an APR of 4.2% to make the purchase. What is the total amount she will spend for the home and how much is the finance charge? 
  • One of the first steps would be to calculate the monthly payment for her mortgage. 

• To determine the total amount paid on the loan, students will multiply the monthly payment by the total number of payments 12⋅30 = 360
  
  $1,149.19 × 360 = $413,708.50 

• Finally, to determine the finance charge (total cost of loan) subtract the purchase price from the total amount paid on the loan. 
  
  $413,708.50 − $235,000 = $178,708.50 

• Finance charges on a credit card are calculated at the end of each billing cycle (usually monthly). The APR for the credit card is applied to the average daily balance of the credit card over the billing cycle, not the final balance at the end of the month. Finding the average daily balance of the credit card will require knowing the balance of the card for each day of the month. 
  • For example, for a 30-day billing cycle, the daily balances for a credit card that has an APR of 24.99% might be: 
    
    
    

• The sum of the balances is $19,029. Divide this by 30 to get $634.30, the average daily balance. 
• To calculate the finance charge for the billing cycle, multiply the average daily balance by the periodic interest rate. Periodic rates are equal to the annual percentage rate divided by the number of periods interest is applied during the year. In this case, the APR should be divided by 12 since the periodic rate is applied monthly. 
  • $r$ = 24.99% ÷ 12 = 2.0825% 
  • $634.30 × 0.020825 ≈ $13.21 
• So, the finance charge for this billing cycle would be $13.21. 
• Since the finance charges of credit cards are based on the average of the balances across the billing cycle, the timing of a purchase in the billing cycle directly affects the finance charge at the end of the month. Large purchases made at the beginning of a billing cycle would increase the average daily balance more than those made toward the end of a billing cycle. This variability makes interpreting word problems involving credit cards difficult. For the purposes of this course, assume credit card purchases in provided examples are made on the first day of the billing cycle, with an initial balance of $0 on the card, and are the only purchases for the billing period. 
• Most credit cards charge interest to the average daily balance of the account over the billing period. Students analyzing the cost of purchasing larger items with a credit card will need to factor other items that may have been or may be purchased with the credit card into account when analyzing repayment calculations.

Common Misconceptions or Errors

• Given the complexity of the formulas used in this benchmark, be sure to calculate one example by hand and by technology to confirm any formulas entered into spreadsheet technology are calculating correctly.

Instructional Tasks

• Calculate the finance charge each month and the total amount paid for 10 months if you charged $2,500 on your credit card that has an annual finance rate of 21.99%. 
• Part A. If you can only afford to pay $250 each month, how long would it take to pay off the charge and fees accrued? 
• Part B. Is it possible to pay off the charge and fees accrued within the 10 months? 

• Omar takes out a 30-year mortgage for $250,000 at a rate of 4.62%. Shanti takes out a 15-year mortgage for $250,000 at a rate of 4.68%. 
• Part A. Calculate the total finance charges of each loan. 
• Part B. Compare the two mortgages.

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