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Lesson 6.7_Simple Interest Students will be able to use proportional relationships to solve multistep ratio and percent problems CCSS. 7.RP.3

Warm-Up #17 (4/4/17) You bought dinner for $20. You gave a 15% tip. How much tip did you leave? Rick bought 2 shirts for $15 each. The sales tax rate is 8.5%. How much did he pay? It costs $10 to make a skateboard. The retailer wants to mark up 80%. What is the sale price?

Homework (4/3/17)  Worksheet: Tax and Tips (Percent) Word Problems (4/4/17)  Textbook: page 256. #5-23 ODD

is money added onto the original amount saved (earned) or borrowed (charged). Simple Interest

I = PRT I = interest earned (amount of money the bank pays you) P = Principle amount invested or borrowed. R = Interest Rate usually given as a percent (must changed to decimal before plugging it into formula) T = Time (must be measured in years) or converted to years by dividing by 12 months

I = PRT Solve for one of variables: To solve for missing variable you must: Plug in what you know Use order of operations

Converting Change % to decimal 1) 12% 2) 5% 3) 2 ½ % 4) 8.5% Change from decimal to % 5) .098 6) .455 Answers 1) .12 2) .05 3) .025 4) .085 5) 9.8% 6) 45.5% Move 2 places to left & drop % sign Move 2 places to right & add % sign

Calculating Simple Interest How much money would you pay in interest if you borrowed $1,600 for 1 ½ years at 16% APR? Convert the percent to a decimal. 16% = 0.16 I = prt I = ($1,600)(0.16)(1.5) I = $384 Total balance: 1600+384=$ 1984

Molly bought a beautiful house for $350,000 Molly bought a beautiful house for $350,000. Her loan was for 30 years at 6.5% APR (annual percentage rate). How much money will she end up paying in interest? 6.5% = 0.065 I = prt I = ($350,000)(0.065)(30) I = $682,500 Total Balance: 350,000+682,500= $1,032,500

Kent put $8,500 into an 18 month CD. The interest rate is 3 Kent put $8,500 into an 18 month CD. The interest rate is 3.25% How much money will Kent earn in interest? 3.25% = 0.0325 I = prt I = ($8,500)(0.0325)(1.5) I = $414.38 Total balance: 8,500+414.38=$8,914.38

Katie bought a new sports car for $28,500 Katie bought a new sports car for $28,500. She financed her car for 6 years at 6.75%APR. How much will she end up paying for interest on her car? 6.75% = 0.0675 I = prt I = $28,500 x .0675 x 6 I = $11,542.50

Cody bought a new truck for $25,000 Cody bought a new truck for $25,000. He took out a loan for 5 ½ years with 7.75% APR. How much will Cody end up paying in interest? 7.75% = 0.0775 I = prt I = ($25,000)(0.0775)(5.5) I = $10,656.25

Tia saved her $9,000 for 2 ½ years at 4 Tia saved her $9,000 for 2 ½ years at 4.25% APR in a CD, to go on a month long vacation with her family. How much did she earn in interest? 4.25% = . 0425 I = prt I = $9,000 x .0425 x 2.5 I = $956.25

Interest paid by bank is unknown Principle (invested) 1. A savings account is set up so that the simple interest earned on the investment is moved into a separate account at the end of each year. If an investment of $5,000 is invested at 4.5%, what is the total simple interest accumulated in the checking account after 2 years. Interest paid by bank is unknown Principle (invested) Rate changed to decimal Time is 2 years Multiply I = PRT I= I=$450 (5,000) (.045) (2)

Interest paid by bank is unknown Principle (invested) 2. A savings account is set up so that the simple interest earned on the investment is moved into a separate account at the end of each year. If an investment of $7,000 is invested at 7.5%, what is the total simple interest accumulated in the checking account after 3 years. I = PRT I= I=$1575 Interest paid by bank is unknown Principle (invested) Rate changed to decimal Time is 3 years Multiply (7,000) (.075) (3)

Principle (invested) is unknown Rate changed to decimal Time is 1 year 3. When invested at an annual interest rate of 6% an account earned $180.00 of simple interest in one year. How much money was originally invested in account? I = PRT 180= 180 = .06P .06 .06 3,000 = P Interest paid by bank Principle (invested) is unknown Rate changed to decimal Time is 1 year Multiply Divide P (.06) (1)

Principle (invested) is unknown Rate changed to decimal Time is 1 year 4. When invested at an annual interest rate of 7% an account earned $581.00 of simple interest in one year. How much money was originally invested in account? I = PRT 581= 581 = .07P .07 .07 $8,300 =P Interest paid by bank Principle (invested) is unknown Rate changed to decimal Time is 1 year Multiply Divide P (.07) (1)

5. A savings account is set up so that the simple interest earned on the investment is moved into a separate account at the end of each year. If an investment of $7,000 accumulate $910 of interest in the account after 2 years, what was the annual simple interest rate on the savings account? I = PRT 910= 910 = (7,000)(2)R 910 = 14,000 R 14,000 14,000 0.065 = R 6.5% = R Interest paid by bank Principle (invested) Rate is unknown Time is 2 years Regroup & Multiply Divide Change to % (7,000) (R) (2)

6. A savings account is set up so that the simple interest earned on the investment is moved into a separate account at the end of each year. If an investment of $2,000 accumulate $360 of interest in the account after 4 years, what was the annual simple interest rate on the savings account? I = PRT 360= 360 = (2,000)(4)R 360 = 8,000 R 8,000 8,000 0.045 = R 4.5% = R Interest paid by bank Principle (invested) Rate is unknown Time is 4 years Regroup & Multiply Divide Change to % (2,000) (R) (4)

Interest paid by bank Principle (invested) Rate is unknown 7. Sylvia bought a 6-month $1900 certificate of deposit. At the end of 6 months, she received a $209 simple interest. What rate of interest did the certificate pay? Interest paid by bank Principle (invested) Rate is unknown Time is 6 months (divide by 12) Regroup & Multiply Divide Change to % I=PRT 209= 209=(1900)(6/12)R 209=950R 950 0.22 = R 22% = R 1900 (R) (6/12)

Interest paid by bank - Unknown Principle (invested) Rate is .045 8. An investment earns 4.5% simple interest in one year. If the money is withdrawn before the year is up, the interest is prorated so that a proportional amount of the interest is paid out. If $2400 is invested, what is the total amount that can be withdrawn when the account is closed out after 2 months? Interest paid by bank - Unknown Principle (invested) Rate is .045 Time is 2 months (divide by 12) Multiply Now, since the money is being withdrawn, add the interest to the principal. I=PRT I= (2400) (.045) (2/12) I=$18 $18 + $2400 = $2418 $2418 will be withdrawn