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Mastering Installment Loans: Solving Problems & Calculating Payments

Learn to solve fixed and open-ended installment loan problems, understand Total Installment Price, early repayment options, and Actuarial Method. Master installment payment formula for financial control.

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Mastering Installment Loans: Solving Problems & Calculating Payments

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  1. Section 10.4 Installment Buying

  2. What You Will Learn • Upon completion of this section, you will be able to: • Solve problems involving fixed installment loans. • Solve problems involving open-ended installment loans.

  3. Installments • A fixed installment loanis one on which you pay a fixed amount of money for a set number of payments. • Examples: college tuition loans, loans for cars, boats, appliances, furniture, etc. • They are usually repaid in 24, 36, 48 or 60 months.

  4. Installments • An open-ended installmentloanis a loan on which you can make variable payments each month. Example: credit cards

  5. Truth in Lending Act in 1968 • This law requires that the lending institution tell the borrower two things: • The annual percentage rate (APR) is the true rate of interest charged for the loan. • The total finance chargeis the total amount of money the borrower must pay for borrowing the money: interest plus any additional fees charged.

  6. Total Installment Price • The total installment price is the sum of all the monthly payments and the down payment, if any.

  7. Table 10.2

  8. Installment Payment Formula • m is the installment payment • p is the amount financed • r is the APR as a decimal • n is the number of payments per year • t is the time in years

  9. Example 2: Using the Installment Payment Formula • Kristin wishes to purchase new window blinds for her house at a cost of $1500. The home improvement store has an advertised finance option of no down payment and 6% APR for 24 months. • Determine Kristin’s monthly payment.

  10. Example 2: Using the Installment Payment Formula • Solution • p = $1500, APR = 0.06, n =12, t = 2

  11. Example 2: Using the Installment Payment Formula • Solution Thus, Kristin’s monthly payment would be $66.48.

  12. Repaying an Installment Loan Early • By paying off a loan early, one is not obligated to pay the entire finance charge. • The amount of the reduction of the finance charge from paying off a loan early is called the unearned interest.

  13. Repaying an Installment Loan Early • Two methods are used to determine the finance charge when you repay an installment loan early. • The actuarial methoduses the APR tables. • The rule of 78sdoes not use the APR tables, is less frequently used, and is outlawed in much of the country.

  14. Actuarial Method for Unearned Interest • u is unearned interest • n is # of remaining monthly payments • P is the monthly payment • V is the value from the APR table for the # of remaining payments

  15. Example 5: Using the Actuarial Method Tino borrowed $9800 to purchase a classic 1966 Ford Mustang. The APR is 7.5% and there are 48 payments of $237. Instead of making his 30th payment of his 48-payment loan, Tino wishes to pay his remaining balance and terminate the loan.

  16. Example 5: Using the Actuarial Method a) Use the actuarial method to determine how much interest Tino will save (the unearned interest, u) by repaying the loan early. Solution n = 18, P = $237, from Table 10.2, using 18 payments and 7.5% APR, we find V = 6.04

  17. Example 5: Using the Actuarial Method Solution n = 18, P = $237, V = 6.04 Tino will save $242.99 in interest by the actuarial method.

  18. Example 5: Using the Actuarial Method b) What is the total amount due to pay off the loan early on the day he makes his final payment? Solution Remaining payments including interest total 18($237) = $4266, his remaining balance excluding his 30th payment is $4266 – $242.99 = $4023.01

  19. Example 5: Using the Actuarial Method Solution A payment of $4023.01 plus the 30th monthly payment of $237 will terminate Tino’s loan. The total amount due is $4023.01 + $237 = $4260.01.

  20. Open-End Installment Loan • A credit card is a popular way of making purchases or borrowing money. • Typically, credit card accounts report: *These rates vary with different credit card accounts and localities.

  21. Open-End Installment Loan • Typically, credit card monthly statements contain the following information: • balance at the beginning of the period • balance at the end of the period (or new balance) • the transactions for the period • statement closing date (or billing date) • payment due date • the minimum payment due

  22. Open-End Installment Loan • For purchases, there is no finance or interest charge if there is no previous balance due and you pay the entire new balance by the payment due date. • The period between when a purchase is made and when the credit card company begins charging interest is called the grace period and is usually 20 to 25 days.

  23. Open-End Installment Loan • However, if you use a credit card to borrow money, called a cash advance, there generally is no grace period and a finance charge is applied from the date you borrowed the money until the date you repay the money.

  24. Average Daily Balance • Many lending institutions use the average daily balance method of calculating the finance charge because they believe that it is fairer to the customer. • With the average daily balance method, a balance is determined each day of the billing period for which there is a transaction in the account.

  25. Example 8: Finance Charges Using the Average Daily Balance Method • The balance on Min’s credit card account on July 1, the billing date, was $375.80. The following transactions occurred during the month of July.

  26. Example 8: Finance Charges Using the Average Daily Balance Method • a) Determine the average daily balance for the billing period. • Solution • (i) find the balance by date

  27. Example 8: Finance Charges Using the Average Daily Balance Method • Solution • (ii) Find the number of days that the balance did not change between each transaction. Count the first day in the period but not the last day. • (iii) Multiply the balance due by the number of days the balance did not change. • (iv) Find the sum of the products.

  28. Example 8: Finance Charges Using the Average Daily Balance Method • Solution 31 Sum = $11,134.50

  29. Example 8: Finance Charges Using the Average Daily Balance Method • Solution (v) Divide the sum by the number of days $11,134.50 ÷ 31 = $359.18 The average daily balance is $359.18.

  30. Example 8: Finance Charges Using the Average Daily Balance Method • b) Determine the finance charge to be paid on August 1, Min’s next billing date. Assume that the interest rate is 1.3% per month. • Solution • Use the simple interest formula: • i = prt • = $359.18 × 0.013 × 1 • ≈ $4.67

  31. Example 8: Finance Charges Using the Average Daily Balance Method • c) Determine the balance due on August 1. • Solution • Since the finance charge for the month is $4.67, the balance owed on August 1 is $466.15 + $4.67, or $470.82.

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