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 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 Interest ApproachWhat 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?
6 Calculating Percentages Percentages are used to determine:interest ratesreturn on investmentsdepreciationbirth ratesgradescan you think of others?
7 Percentage = a fraction with a denominator of 100 the denominator the bottom number of a fractionFormula for percentage = A/B x 100 = %Examples9% = 9/10053% = 53/10016.5% = 16.5/100
8 Converting percentages to decimals Always move decimal two places to the left when converting percentages to decimal form.9% = .0953% - .5316.5% = 16.5
10 Applications using percentages example #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 % = .20Step 2: Multiply the value of the barn by the decimal amount. $54,000 × .20 = $10,800 depreciation for this year
11 Applications using percentages example #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 /75 = .92Step 2: Convert the decimal form to a %. Move the decimal point two spaces to the right and add a percent sign (%) = 92%
12 Applications using percentages example #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 % = .15Step 2: Multiply the regular price of the oil by the sale discount × .15 = $7.20 discountStep 3: Subtract the discount from the regular price of the oil. $48.00 – $7.20 = $40.80 price you will pay with the discount
13 Applications using percentages example #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 decreaseStep 2: Divide the per acre decrease by the price from last year. $450 per acre decrease/$2,800 per acre last year value = .1607Step 3: Move the decimal point two spaces to the right and add a percent sign = 16.07% decrease in value of farm real estate
14 Calculating Interest Interest - the cost of money Simple Interest (Add-in method)only uses the original principal amount to determine interestformula to determine interestPrincipal x Rate x TimePrincipal = total amount borrowedrate = interest rate expressed as a percentagetime = number of years the money is being borrowed
15 Determining Simple Interest Example #1 Find the interest amount on $3,000 at 8% interest for one year.Step 1: Interest = principal × rate × timeStep 2: Interest = 3,000 × .08 × 1Convert 8% to decimal form (.08) for formula.Step 3: Interest = $240 paid for the use of $3,000 for one year.
16 Determining Simple Interest Example #2 Find the future value of $5,000 invested at 6% for three years using simple interest.Step 1: Interest earned = principal × rate × timeStep 2: Interest earned = 5,000 × .06 × 3 =$900Convert 6% to decimal form (.06) for formula.Step 3: Future value = interest earned + principalFV = $900 + $5,000FV = $5,900.00
17 Determining Simple Interest Example #3 Find the interest on $2,000 borrowed at 9% for 73 days.Step 1: Interest = principal × rate × timeStep 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 × .20Interest = $36.00
18 Compound Interest Results in higher payments accrues “interest on interest”can be compounded annually, semiannually, monthly, or dailyFormula for determining future using compound interest =FV = Present Value x (1+rate) x term
19 Determining Compound Interest Example 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 × ( ) 5FV = 1,000 × (1.08 × 1.08 × 1.08 × 1.08 × 1.08)FV = 1,000 ×FV = $1,469.33Step 3. The interest earned can be calculated by subtracting the original investment of $1,000 from the future value of $1, Therefore, the amount of compounded interest earned in this example is $
20 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.