Chapter 8 LOANS

Think… Picture a world where loans don’t exist…. What types of things would be more difficult or impossible for the average person to purchase?

Discuss Has anyone ever loaned money to someone? How long did it take to be paid back? Was it paid back in one payment?

8.1 – Single Payment Loans Single Payment Loan – a loan that you repay with one payment after a specified period of time Promissory Note – a type of single payment loan Written promise to pay a certain sum of money on a certain date in the future

8.1 – Single Payment Loans Maturity Value – the total amount of the loan that you must repay Includes both the principal and the interest owed Term (of a loan) – the amount of time for which the loan is granted

How to Calculate Interest Ordinary Interest – calculated by basing the time of the loan on a 360-day year Exact Interest – calculated by basing the time of the loan on a 365-day year

Equations Interest = Principal x Rate x Time Ordinary Interest Exact Interest = Principal x Rate x Time ÷ 365 Maturity Value = Principal + Interest Owed

Think… Why might banks want to use ordinary interest (360-day year) as opposed to exact interest (365-day year)? Suppose you borrow $1000 for 90 days at 12% OI: ($1000)x(0.12)x(90÷360) = $1030 EI: ($1000)x(0.12)x(90÷365) = $1029.59

Example 1 Emma’s bank granted her a single-payment loan of $7,200 for 91 days at 12% ordinary interest. What is the maturity value of the loan? Find the interest I=(PRT)÷(360) = (7,200)(.12)(91÷360) = $218.40 Maturity Value = P + I = $7,200 + $218.40 = $7,418.40

Example 2 Suppose Emma’s bank granted her a single-payment loan of $7,200 for 91 days at 12% exact interest. What is the maturity value of the loan? I = $7,200(0.12)(91/365) = $215.41 Maturity Loan=$7,200 + $215.41 = $7,415.41

Questions? Page 285, #1-16 Show me your work when you finish and I will give you your homework!!!

8.2 – Installment Loans Installment Loan – A loan that you repay in several equal payments over a specified period of time Usually have to make a down payment Down Payment – a portion of the cash price of the item you are purchasing Amount Financed – portion of the cash price that you owe after making the down payment

Installment Loans Amount Financed = Cash Price – Down Payment Down Payment = Amount x Percent

Reasons for borrowing money? Car Furniture Appliance School House Other expensive consumer items

Example 1 Tanya is buying a new refrigerator for $1,399. She made a down payment of $199 and financed the remainder. How much did Tanya finance? Cash Price – Down Payment $1,399 – $199 = $1,200 financed

Example 2 Purchase washer/dryer for $1,140. Used the store’s installment credit plan to pay. Made a down payment and financed remaining amount. What amount was financed if a 20% down payment was made? Find the 20% down payment ($1,140 x 0.20) = $228 Find the amount financed $1,140 - $228 = $912 financed

8.3 – Simple Interest Installment Loans Simple Interest Installment Loan – A loan repaid with equal monthly payments Must pay finance charges for the use of money Part of each payment is used to pay interest

8.3 – Simple Interest Installment Loans Annual Percentage Rate – an index showing the relative cost of borrowing money Monthly Payment = (Amount of Loan) x Monthly Payment ($100) for a $100 loan

8.3 – Simple Interest Installment Loans Total Amount Repaid = (Number of Payments) x (Monthly Payments) Finance Charge = (Total Amount Repaid) - (Amount Financed)

Example 1 Clarissa obtained an installment loan of $1,800 to purchase new furniture. The APR is 8%. She must repay the loan in 18 months. What’s the finance charge? Find monthly payment (pg. 799) ($1,800/$100) x $5.91 = $106.38 Find total amount repaid 18 months x $106.38 = $1,914.84 Find the finance charge $1,914.84 - $1,800.00 = $114.84 finance charge

Example 2 Buying a new oven with installment loan, APR rate of 12%. Oven sells for $1,399.99. Store financing requires a 10% down payment and 12 monthly payments. Find finance charge. Find amount Financed $1,399.99 – (0.10 x 1,399.99) = $1,259.99 Find monthly Payment ($1259.99/$100) x $8.88 =$111.89 monthly payment Find total amount repaid: 12 x $111.89 = $1,342.68 Find finance charge $1,342.68 - $1,259.99 = $82.69 finance charge

8.4 – Installment Loans: Allocation of Monthly Payment Repayment Schedule – shows the distribution of interest and principal over the life of a loan

Payment Number Monthly Payment Amount for Interest Repayment Schedule for a $1,800 Loan at 8.0% for 6 Months Payment Number Monthly Payment Amount for Interest Amount for Principal Balance $1,800 1 $307.08 $12.00 $295.08 $1,504.92 2 307.08 10.03 297.05 1,207.87 3 8.05 299.03 908.85 4 6.06 301.02 607.82 5 4.05 303.03 304.80 6 306.83 2.03 0.00

Formulas Interest = Principal x Rate x Time Payment to Principal = Monthly Payment – Interest New Principal = Previous Principal – Payment to Principal

Take out a loan of $1,800 at 8% for 6 months shown in the repayment schedule (previous slide or pg. 294). Show the calculation for the first payment. What is the interest? What is the payment to principal? What is the new principal? Find interest $1,800 x 0.08 x (1/12) = $12.00 interest Find payment to principal $307.08 - $12.00 = $295.08 payment to principal Find new principal $1,800 - $295.08 = $1,504.92 new principal

Obtain a loan of $6,000 at 8% for 36 months. Monthly payment is $187 Obtain a loan of $6,000 at 8% for 36 months. Monthly payment is $187.80. The balance of the loan after 20 payments is $2,849.08. What is the interest for the first payment? The 21st payment? Find interest for the 1st payment $6,000 x 0.08 x (1/12) = $40.00 Find interest for the 21st payment $2,849.08 x 0.08 x (1/12) = $18.99

HOMEWORK

8.5 – Paying Off Simple Interest Installment Loans Final Payment – payment on a simple interest loan that consists of the remaining balance plus the current month’s interest The reason to pay off a loan before the end of the term is to pay less interest

Formulas Final Payment = Previous Balance + Current Month’s Interest Interest Saved = Total Payback - (sum of previous payments + final payment)

You have a loan in which the previous balance is $5,000 at 12% interest. Find the interest and the final payment. Interest = P x R x T I = ($5,000)x(0.12)x(1/12) = $50.00 Final Payment = Previous + Current month’s balance interest Final Payment = $5,000 + 50 = $5,050 final payment

Take out a simple interest loan of $6,000 at 10% for 24 months Take out a simple interest loan of $6,000 at 10% for 24 months. Monthly payment is $276.60. After 4 payments, balance is $5,082.21. You pay off the loan when the next payment is due.What is the interest? What is the final payment? How much do you save by paying off the loan early? I = ($5,082.21)x(0.10)(1/12) = $42.35 Final Pay = $5,082.21 + $42.35 = $5,124.56 INTEREST SAVED Total Payback – (sum of prev. pay + final payment) 24 x 276.60 – [(4 x 276.60) + 5,124.56] $6,638.40 – ($1,106.4 + $5,124.56) = $407.44

8.6 – Determining the APR If you know the # of monthly payments and the finance charge per $100 of the amount financed, you can use a table to find the APR of the loan Finance Charge per $100 = $100 x (Finance Charge ÷ Amount Financed)

Example Chuck Norris obtained an installment loan of $1,500.00 to pay for a computer. The finance charge is $146.25. He agreed to repay the loan in 18 monthly payments. What is the annual percentage rate? Find finance charge per $100 $100 x ($146.25 ÷ $1,500) =$100 x (0.0975) = $9.75 Find APR using table given In the row for 18 payments, find the number closest to $9.75 12% APR

A 54-inch HDTV is for sale for $1,899. 92 cash or $177 A 54-inch HDTV is for sale for $1,899.92 cash or $177.83 per month for 12 months. What is the APR? Find interest (total payback – amount financed) (12 x $177.83) - $1,899.92 = $234.04 Find finance charge per $100 $100 x (234.04 ÷ $1,899.92) = $12.32 Use the table to find the APR APR of 22%