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Lesson. Calculating Interest Rates. Next Generation Science /Common Core Standards Addressed!.

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  1. Lesson Calculating Interest Rates

  2. Next Generation Science /Common Core Standards Addressed! • CCSS.Math.Content.7.R P.A.3Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest,tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percenterror.

  3. Agriculture, Food and Natural Resource Standards Addressed! • CRP.08.03. Establish plans to solve workplace and community problems and execute them with resiliency. • CRP.08.03.02.a. Identify and analyze the elements of a plan for solving workplace and community problems (e.g., budget, timeline, etc.).

  4. Bell Work/ Student Learning Objectives • Describe percentages and how they are calculated. • Explain applications using percentages. • Explain how to calculate interest. • Discuss applications using interest calculation in agricultural business management.

  5. Compound interest Denominator Interest Interest rate Percentage Principal Rate Ratio Simple interest Time Terms

  6. Interest Approach • What are some agricultural occupations which might require calculating interest rates? • What are some situations that might require the need to figure interest cost? • What are the different kinds of interest rates?

  7. Calculating Percentages • Percentages are used to determine: • interest rates • return on investments • depreciation • birth rates • grades • can you think of others?

  8. Percentage = a fraction with a denominator of 100 • The denominator the bottom number of a fraction. • Formula for percentage = A/B x 100 = % • Examples • 9% = 9/100 • 53% = 53/100 • 16.5% = 16.5/100

  9. Converting percentages to decimals • Always move decimal two places to the left when converting percentages to decimal form. • 9% = .09 • 53% - .53 • 16.5% = 16.5

  10. Converting fractions to percentages • 1/4 = 25/100 = 25% • 3/5 = 60/100 = 60% • 13/10 = 130/100 = 130% • 37/50 = 74/100 = 74%

  11. Applications using percentagesexample #1 • You want to depreciate a newly constructed barn that has been valued at $54,000. Your depreciation schedule recommends 20% depreciation this year. How will you determine that value? • Step 1: Convert the depreciation percentage to a decimal 20% = .20 • Step 2: Multiply the value of the barn by the decimal amount. $54,000 × .20 = $10,800 depreciation for this year

  12. Applications using percentagesexample #2 • You have a herd of 75 beef cows that are calving. Out of the 75 cows, 69 had live calves. How would you determine the birth rate percentage for your herd? • Step 1: Divide the number of live calves by the number of cows. 69/75 = .92 • Step 2: Convert the decimal form to a %. Move the decimal point two spaces to the right and add a percent sign (%). .92 = 92%

  13. Applications using percentagesexample #3 • Your local farm supply company has a special discount of 15% on oil. What is the net sale amount of a case of oil regularly priced at $48.00? • Step 1: Convert the discount percentage to a decimal.15% = .15 • Step 2:Multiply the regular price of the oil by the sale discount.48.00 × .15 = $7.20 discount • Step 3:Subtract the discount from the regular price of the oil.$48.00 – $7.20 = $40.80 price you will pay with the discount

  14. Applications using percentagesexample #4 • According to a recent publication, farm real estate values in your county have dropped from $2,800 per acre last year to $2,350 per acre this year. What is the percentage change in real estate value between those two years? • Step 1: Subtract the price per acre this year from the price last year. $2,800 per acre – $2,350 per acre = $450 per acre decrease • Step 2: Divide the per acre decrease by the price from last year. $450 per acre decrease/$2,800 per acre last year value = .1607 • Step 3: Move the decimal point two spaces to the right and add a percent sign. 0.1607 = 16.07% decrease in value of farm real estate

  15. Calculating Interest • Interest - the cost of money • Simple Interest (Add-in method) • only uses the original principal amount to determine interest • formula to determine interest • Principal x Rate x Time • Principal = total amount borrowed • rate = interest rate expressed as a percentage • time = number of years the money is being borrowed

  16. Determining Simple InterestExample #1 • Find the interest amount on $3,000 at 8% interest for one year. • Step 1: Interest = principal × rate × time • Step 2: Interest = 3,000 × .08 × 1 • Convert 8% to decimal form (.08) for formula. • Step 3: Interest = $240 paid for the use of $3,000 for one year.

  17. Determining Simple InterestExample #2 • Find the future value of $5,000 invested at 6% for three years using simple interest. • Step 1: Interest earned = principal × rate × time • Step 2: Interest earned = 5,000 × .06 × 3 =$900 • Convert 6% to decimal form (.06) for formula. • Step 3: Future value = interest earned + principal • FV = $900 + $5,000 • FV = $5,900.00

  18. Determining Simple InterestExample #3 • Find the interest on $2,000 borrowed at 9% for 73 days. • Step 1: Interest = principal × rate × time • Step 2: Interest = 2,000 × .09 × (73/365) • Convert 9% to decimal form (.09) for formula. • Convert 73 days to years by dividing by 365 days/year. • Step 3: Interest = 2,000 × .09 × .20 • Interest = $36.00

  19. Compound Interest • Results in higher payments • accrues “interest on interest” • can be compounded annually, semiannually, monthly, or daily • Formula for determining future using compound interest = • FV = Present Value x (1+rate) x term

  20. Determining Compound InterestExample • You invest $1,000 at 8% compounded annually for five years. What is the future value? • Step 1. Future value = present value × (1 + rate) n. The reinvested amount is represented as 1 within the formula; n = number of years. • Step 2. FV = 1,000 × (1 + .08) 5 • FV = 1,000 × (1.08 × 1.08 × 1.08 × 1.08 × 1.08) • FV = 1,000 × 1.46933 • FV = $1,469.33 • Step 3. The interest earned can be calculated by subtracting the original investment of $1,000 from the future value of $1,469.33. Therefore, the amount of compounded interest earned in this example is $469.33.

  21. Review • Describe percentages and how they are calculated. • Explain applications using percentages. • Explain how to calculate interest. • Discuss applications using interest calculation in agricultural business management.

  22. The End!

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