BUS250

Seminar 6

Key Terms• Interest: an amount paid or earned for the use

of money.

• Simple interest: interest earned when a loan or investment is repaid in a lump sum.

• Principal: the amount of money borrowed or invested.

• Rate: the percent of the principal paid as interest per time period.

• Time: the number of days, months or years that the money is borrowed or invested.

11.1.1 The Simple Interest Formula

• The interest formula shows how interest, rate, and time are related and gives us a way of finding one of these values if the other three values are known.

I = P x R x T

Try these examples• Find the interest on a 2-year loan of

$4,000 at a 6% rate.• $480

• Find the interest earned on a 3-year investment of $5,000 at 4.5% interest.

• $675

Look at this example• Marcus Logan can purchase furniture on a

2-year simple interest loan at 9% interest per year.

• What is the maturity value for a $2,500 loan?

• MV = P (1 + RT) Substitute known values.

• MV = $2,500 ( 1 + 0.09 x 2)

(See next slide)

What is the maturity value?• MV = $2,500 ( 1 + 0.09 x 2)

• MV = $2,500 (1 + 0.18)

• MV = $2,500 (1.18)

• MV = $2,950

• Marcus will pay $2,950 at the end of two years.

Try these examples• Terry Williams is going to borrow $4,000 at 7.5%

interest. What is the maturity value of the loan after three years?

• $4,900

• Jim Sherman will invest $3,000 at 8% for 5 years. What is the maturity value of the investment?

• $4,200

Look at this example• To save money, Stan Wright invested $2,500

for 42 months at 4 ½ % simple interest. How much interest did he earn?

• 42 months = 42/12 = 3.5

• I = P x R x T

• I = $2,500 x 0.045 x 3.5

• I = $393.75

• Stan will earn $393.75

Try these examples

• Akiko is saving a little extra money to pay for her car insurance next year. If she invests $1,000 for 18 months at 4%, how much interest can she earn?

• $60

• Habib is going to borrow $2,000 for 42 months at 7% . What will the amount of interest owed be?

• $490

Find the principal using the simple interest formula

• P = I / RT

• Judy paid $108 in interest on a loan that she had for 6 months. The interest rate was 12%. How much was the principal?

• Substitute the known values and solve.

• P = 108/ 0.12 x 0.5

• P = $1,800

• R = I / PT

• Sam wants to borrow $1,500 for 15 months and will have to pay $225 in interest. What is the rate he is being charged?

• Substitute the known values and solve.

• R = 225/ $1,500 x 1.25

• R = .12 or 12%

• The rate Sam will pay is 12%.

Find the rate using the simple interest formula

11.2.1 Find Exact Time

• Ordinary time: time that is based on counting 30 days in each month.

• Exact time: time that is based on counting the exact number of days in a time period.

11.2.3 Find the Ordinary Interest and the Exact Interest

• Ordinary interest: a rate per day that assumes 360 days per year.

• Exact interest: a rate per day that assumes 365 days per year.

• Banker’s rule: calculating interest on a loan based on ordinary interest and exact time which yields a slightly higher amount of interest.

Try this example• What is the effective interest rate of a $5,000

simple discount note, at an ordinary bank discount rate of 12%, for 90 days?

• I = PRT; I = $5,000(.12)(90/360)• I = $150 (Bank discount)• Proceeds = $5,000 - $150 = $4,850• R = I/PT; R = $150/$4,850(90/360)• R = .1237113402

• R or the effective interest rate = 12.4%

Key Terms

• Consumer credit: a type of credit or loan that is available to individuals or businesses. The loan is repaid in regular payments.

• Installment loan: a loan that is repaid in regular payments.

• Closed-end credit: a type of installment loan in which the amount borrowed and the interest is repaid in a specific number of equal payments.

• Open-end credit: a type of installment loan in which there is no fixed amount borrowed or number of payments. Regular payments are made until the loan is paid off.

• Finance charges or carrying charges: the interest and any fee associated with an installment loan.

Key Terms

Try this example

• Karen purchased a copier on the installment plan with a down payment of $50 and 6 monthly payments of $29.95. Find the installment price.

• $229.70

Look at this example

• The installment price of a pool table was $1,220 for a 12-month loan. If a $320 down payment was made, find the installment payment.

• Installment Price = $1,220

• $1,220 - $320 = $900 [$320 is the down payment.]

• $900 ÷ 12 = $75

• The installment payment is $75

12.1.3 Find the Estimated APR Using a Table

• Annual percentage rate (APR): the true rate of an installment loan that is equivalent to an annual simple interest rate.

• Truth in Lending Act: passed in 1969 by the federal government, it requires a lending institution to tell the borrower in writing what the APR actually is.

Annual Simple Interest Rate Equivalent

• Example: If you borrowed $1,500 for one year and were charged $165 in interest, you would be paying an interest rate of 11% annually.

• $165 ÷ $1,500 = 0.11 = 11%

• If you paid the money back in 12 monthly installments of $138.75, you would not have use of the entire $1,500 for a full year.

• In effect you would be paying more than the 11% annually.

Percentage rate tables

• The APR can be determined using a government-issued table.

• APR rates are within ¼ % which is the federal standard.

• A portion of one of these tables based on the number of monthly payments is shown in your text in Table 12-1.

Look at this example

• Lewis Strang bought a motorcycle for $3,000, which was financed at $142 per month for 24 months. There was no down payment.

• Find the APR.

• Installment price = $142 x 24 = $3,408

• Finance charge = $3,408 - $3,000 = $408