Calculating Interest Rates Lesson Calculating Interest Rates

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.

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.

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

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?

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

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

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

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

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 20% = .20 Step 2: Multiply the value of the barn by the decimal amount. $54,000 × .20 = $10,800 depreciation for this year

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. 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%

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. 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

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 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

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

Determining Simple Interest Example #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.

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 × 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

Determining Simple Interest Example #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

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

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 × (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.

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.

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