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APR and Rule of 78 Calculation for Finance Charges

Learn how to calculate the charge per $100 financed and the APR using the Rule of 78 and formula methods. Examples provided.

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APR and Rule of 78 Calculation for Finance Charges

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  1. 13.3 Annual Percentage Rate (APR) and the Rule of 78 1

  2. Page 910: Charge per $100 financed Jimmie bought new electronic equipment for his business for $7325. He agreed to pay 50 monthly payments of $188.80. Find the charge per $100 financed. Payments 50 x $188.80 = $9440.00 Amount financed 7325.00 Finance charge $2115.00 Finance charge per $100 2

  3. Finding the APR using the table on page 909 Jimmie bought new electronic equipment for his business for $6324. He agreed to pay 42 monthly payments of $198.75. What was the APR on this purchase? Payments 42 x $198.75 = $8347.50 Amount financed 6324.00 Finance charge $2023.50 Finance charge per $100 APR = 16  % 3

  4. Finding the APR using the table on page 909 Jimmie bought new electronic equipment for his business for $6324. He agreed to pay 42 monthly payments of $198.75. What was the APR on this purchase? Payments 42 x $198.75 = $8347.50 Amount financed –6324.00 Finance charge $2023.50 Finance charge per $100 4

  5. Page 917: Approximating the APR by Formula m = the number of payment periods per year I = the interest (or finance charge) P = the principal ( amount financed) n = the number of periodic payments to be made 5

  6. Suppose you purchase furniture for $2100. You pay 16% down and sign a contract to repay the balance in 28 equal monthly payments. The finance charge on the balance is 8.9% simple interest. Estimate the APR to the nearest tenth of a percent using the formula. m = 12 P = $2100 – 0.16*$2100 = $1764 I = $1764*0.089 *28/12= $366.324= $366.32 n = 28 6

  7. Finance Charge You take out a consumer loan at your credit union for new insulated windows for your house. The total installed cost is $10,100 of which you pay 14% down. The balance is to be paid in 60 equal monthly payments with a finance charge equal to 9.3% add-on interest on the outstanding balance. Find the finance charge. Principal financed $10,100 – 0.14 x $10,100 = $8686.00 Time 60/12 = 5 years Finance charge 0.093 x $8686.00x 5 = $4039.00 7

  8. Page 912: Formula for Unearned Interest u r is number of remaining payments n is number of payments and F is the finance charge A flower shop owner wants to pay off the loan on a used delivery van that was purchased 16 months ago. The 2-year installment plan used to purchase the van included a $250 finance charge and called for payments of $210 monthly. What amount is needed to pay off the loan? r = 8 n = 24 F = $250 Payment = 8  $210  $30 = $1650.00 8

  9. Monthly Payment You take out a consumer loan at your credit union for new insulated windows for your house. The total installed cost is $3,400 of which you pay 12% down. The balance is to be paid in 24 equal monthly payments with a finance charge equal to 5.4% add-on interest on the outstanding balance. Find the monthly payment. Amount Financed $3400 – 0.12 x $3400 = $2992 Time 24/12 = 2 years Finance charge $2992 x 0.054 x 2 = $323.14 Monthly Payment ($2992.00 + $323.14)/24 = $138.13 9

  10. Page 913: Actuary Formulas for the Refund u and the Payoff The refund u is given by The payoff is given by Where r is the number of remaining payments, PMT is the payment, and V is the value from the APR table corresponding to r. Where PMT is the payment, and r is the number of remaining payments. 10

  11. Example Tony bought a dinette set for $990. The 24 payments were $46.20 each with an APR of 14%. After 18 months, Tony has decided to pay off the loan. Find • the refund using the formula. • the payoff using the formula. r = 6 V = $4.12 11

  12. Finance Charge per $100 If a closed-end loan requires n equal monthly payments and APR denotes the true annual interest rate for the loan (as a decimal), then the finance charge per $100 financed is given by Example Determine the finance charge per $100 financed 69 monthly payments and an APR of 6.2%. 12 END

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