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Calculating Interest Rates

This article discusses the importance of calculating interest rates and how it is applicable in agricultural business management. It covers topics such as percentages, interest calculation, and converting percentages to decimals and fractions. Examples and applications using percentages are also provided. Suitable for mathematics and agriculture education.

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Calculating Interest Rates

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  1. Calculating Interest Rates

  2. Next Generation Science/Common Core Standards Addressed! • CCSS. Math. Content. HSSID.A.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. • CCSS. Math .Content. HSSIC.A.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population

  3. Agriculture, Food and Natural Resource Standards Addressed! • ABS.02.01. Apply fundamental accounting principles, systems, tools and applicable laws and regulations to record, track and audit AFNR business transactions (e.g., accounts, debits, credits, assets, liabilities, equity, etc.). • ABS.02.01.01.b. Evaluate the implementation and appropriateness of accounting systems and procedures used for record keeping in AFNR businesses

  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 • can you think of others?

  8. Percentage = a fraction with a denominator of 100 • the denominator is 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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