11.4 Installment Buying
Open-end installment loan: a loan on which you can make variable
payments each month, e.g. credit cards
Fixed installment loan: a loan on which you pay a fixed amount of money
for a set number of payments, e.g. car loan, traditional house loan
Credit rating: a number assigned to a consumer that indicates the
potential risk of loss or payment due to prior credit behavior of the individual.
Annual Percentage Rate (APR): the true rate of interest charged for a
loan.
Finance Charge: the total amount of money the borrower must pay for the
use of the financial institutions money.
Fixed Installment Loan
Ex 1 Financing a New Boat: Pablo Silonto purchased a new boat for
$45,000. He paid 10% as a down payment and financed the balance of the purchase with a 60-month fixed installment loan with an APR of 6.5%.
a) Determine Pablo’s total finance charge. b) Determine Pablo’s monthly payment. Use the chart on page 680.
Ex 2 Financing a Used Car: Jack wishes to purchase a used car that has a cash price of $12,000. The installment terms include a down payment of $3000 and 48 monthly payments of $224.
a) What finance charge will Jack pay?
Ex 3 Financing Furniture: Mr. and Mrs. Chan want to buy furniture that has a cash price of $3450. On the installment plan they must pay 25% of the cash price as a down payment and make six monthly payments of $437.
a) What finance charge will the Chans pay? b) What is the APR to the nearest half percent?
Two methods used to determine the finance charge when you repay an installment loan early: actuarial method and rule of 78s. The Rule of 78s is no longer used.
P. 682
Actuarial Method Rule of 78s (no longer used)
V V P n u + ⋅ ⋅ = 100 ( 1) ) 1 ( + + ⋅ = n n k k f u
u = unearned interest u = unearned interest n = number of remaining monthly
payments (excluding current payment)
f = original finance charge
P= monthly payment k = number of remaining monthly payments (excluding current payment)
V = the value from the APR table that corresponds to the annual percentage rate for the number of remaining payments (excluding current payment)
Ex 4 Early repayment using the Actuarial Method: Ray Flagg took out a 60-month fixed installment loan of $12,000 to open a pet store. He paid no money down and began making monthly payments of $232. Ray’s business does better than expected and instead of making his 24th payment, Ray wishes to repay his loan in full.
a) Determine the APR of the installment loan.
b) How much interest will Ray save (use the actuarial method). c) What is the total amount due to pay off the loan?
Open – End Installment Loan: a loan like a credit card or line of credit.
There is no due date just a minimum payment required.
In a credit card scenario, there is no finance or interest charge if there is no previous balance due and if you pay the entire new balance by the
payment due date.
For cash advance, a finance charge is applied from the date you borrowed the money until you repay the loan.
Example of Credit Card Terms Table 11.3
Type of Charge Daily Periodic Rate* Annual Percentage Rate* Purchases 0.03490% 12.74%
Cash Advances 0.05477% 19.99% *These rates vary with different charge accounts and localities.
Ex 5 College Expenses: Brian Hickey uses his credit card in August to purchase the following college supplies: books ($425), yearlong
bus pass($175), food service meal ticket ($450), and season tickets to the basketball games ($125). On September 1, he used $650 of his financial aid check to reduce the balance. The issuing bank charges 1.2% interest per month and requires full payment within 36 months. Brian had a
previous balance of zero and he makes no other purchases with this card. a) What is the minimum payment due September 1?
b) What is the balance due on October 1?
When additional charges are made during the period, the finance charge on open-end installment loans or credit cards are generally calculated in one of two ways: the unpaid balance method or the average daily
balance method.
Unpaid Balance Method: The borrower is charged interest or a finance charge on the unpaid balance from the previous charge period.
Ex 6 Unpaid Balance Method: On September 5, the billing date, Verna Brown had a balance due of $567.20 on her credit card. The transactions during the following month were:
September 8 Payment $275.00 September 21 Charge: Airline Ticket $330.00 September 27 Charge: Hotel Bill $190.80 October 2 Charge: Clothing $84.75
a) Find the finance charge on October 5, using the unpaid balance method. Assume that the interest rate is 1.1% per month.
b) Find the new balance on October 5.
Average Daily Balance Method: a balance is determined each day of the
billing period for which there is a transaction in the account.
Ex 7 Average Daily Balance Method: The Levy’s credit card statement shows a balance due of $1578.25 on March 23, the billing date. For the period ending April 23, they had the following transactions.
March 26 Charge: Party Supplies $79.98 March 30 Charge: Restaurant Meal $52.76 April 3 Payment $250.00 April 15 Charge: Clothing $190.52 April 22 Charge: Car Repairs $190.85
a) Find the average daily balance of the billing period.
b) Find the finance charge to be paid on April 23. Assume and interest rate of 1.3% per month.
Ex 8 A Cash Advance: John Richards borrowed $875 against his charge account on September 12 and repaid the loan on October 14 (32 days later). Assume that the interest rate is 0.04273% per day.
a) How much interest did John pay on the loan?
b) What amount did he pay the bank when he repaid the loan?
Ex 9 Comparing Loan Options: Sara Lin wants to purchase a new
television set. The purchase price is $890. If she purchases the set today and pays cash, she must take money out of her savings account. Another option is to charge the TV on her credit card, take the set home today, and pay nest month. Next month she will have cash and can pay her credit card balance without paying any interest. The simple interest rate on her savings account is 5 ¼ %. How much is she saving by using the credit card instead of taking the money our of her savings account?
