1. Review: Mini-Quiz Vector Addition
Redraw the graph using the Polygon Method.
Find the magnitude of the resultant vector to the nearest hundredth.
𝑎 2 + 𝑏 2 = 𝑐 2
𝑎=3 𝑎𝑛𝑑 𝑏=4
𝑐 2 =
𝑐 2 =9+16
𝑐 2 =25
𝑐= 25
𝑐=5

2. Business Math
Simple Interest

3. Class Greeting

4. Objective: The student will be able to find simple interest by using the simple interest formula and find the principal, rate or time using the simple interest formula.

5. 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.

6. 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

7. Find the simple interest using the simple interest formula

8. Identify the principal, rate and time.
I = P x R x T
Interest is an amount that is added to the amount borrowed or invested.
Principal is the amount borrowed or invested.
Rate is a percent.
Time must be expressed in the same unit of time as the rate. (i.e. one year)

9. Find the interest paid on a loan.
Principal = (P) $1,500.
Interest rate = 9% (or 0.09)
Time = 1 year
Interest = P x R x T
Interest = 1,500 x 0.09 x 1
Interest = $135
The interest on the loan is $135.

10. Try this example.
Find the interest on a 2-year loan of $4,000 at a 6% rate.
$480

11. Find the maturity value (MV) of a loan.
Maturity value: the total amount of money due by the end of a loan period; the amount of the loan and interest.
If the principal and the interest are known, add them.
MV = principal + PRT

12. 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 = principal + PRT
MV = $2,500 + $2,500(0.09)(2)
MV = $2,500 + $450
MV = $2,950

13. Try this example.
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

14. Convert months to a fractional or decimal part of a year.
Write the number of months as the numerator of a fraction.
Write 12 as the denominator of the fraction.
Reduce the fraction to lowest terms if using the fractional equivalent.
Divide the numerator by the denominator to get the decimal equivalent of the fraction.

15. Convert the following to fractional or decimal part of a year.
Convert 9 months and 15 months, respectively, to years, expressing both as fractions and decimals.
9/12 = ¾ = 0.75
9 months = ¾ or 0.75 of a year
15/12 = 1 3/12 = 1 ¼ = 1.25
15 months = 1 ¼ or 1.25 of a year.

16. Look at this example.
To save money, Stan Wright invested $2,500 for 45 months at 3 ½ % simple interest. How much interest did he earn?
45 months = 45/12 = 3.75
I = P x R x T
I = $2,500 x x 3.75
I = $328.13
Stan will earn $328.13

17. Try this example.
Habib is going to borrow $2,000 for 42 months at 7% . What will the amount of interest owed be?
$490

18. Find the principal, rate or time using the simple interest formula.

19. 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

20. Find the rate using the simple interest formula.
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%.

21. Find the time using the simple interest formula.
T = I / RP
Shelby borrowed $10,000 at 8% and paid $1,600 in interest. What was the length of the loan?
Substitute the known values and solve.
T = $1,600/0.08 x $10,000
T = 2
The length of the loan was two years.

22. Lesson Summary:
Objective: The student will be able to find simple interest by using the simple interest formula and find the principal, rate or time using the simple interest formula.

23. Preview of the Next Lesson:
Objective: The student will be able to solve Mathematical Problems related to Business and Economics.

24. Mathematical Skills and Processes - HW 10
Homework
Mathematical Skills and Processes - HW 10