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A1.1.E Solve problems that can be represented by exponential functions and equations A1.2.D Determine whether approximations or exact values of real numbers are appropriate, depending on the context, and justify the selection. A1.6.B Make valid inferences and draw conclusions based on data. A1.7.B Find and approximate solutions to exponential equations. Objectives

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Principal: The initial amount of money you invest or borrow Simple Interest: Interest that is calculated based on only the principal and time (in years) **Most financial institutions DO NOT use Simple interest.** Compound Interest: Interest that is calculated based on principal combined with prior interest for a period of time (in years) **Most financial institutions DO use compound interest!** Vocabulary

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APR (Annual Percentage Rate): The actual percent that is accumulated in each period that your interest compounds APY (Annual Percentage Yield): The percent of interest that is expected to accumulate in a year, taking compounding into account. APR vs. APY

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Formula: B = P(1 + r/n) nt Compound Interest Balance Principal APR Number of times it compounds in a year Time in years

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Example: Tom invests $5,000 in a CD for 4 years with an interest rate of 3% compounded monthly. How much will Tom have at the end of 4 years? B = B = $5636.64 Compound Interest 5000 (1+ ) 12 12* 0.03/ 4

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Example: What if Tom can only invest his money for one year? Will he have more money or less? How much? B = 5000(1+0.03/12) 12*1 B = $5152.08 $484.56 less, but he will get his money 3 years sooner. Compound Interest

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Example: What if Tom can only invest his money for 6 months? How much will he earn? B = 5000(1+0.03/12) 12*0.5 B = $5075.47 Compound Interest

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CD’s can compound daily, monthly, or quarterly. Credit cards, checking accounts, savings accounts and money market accounts typically compound daily. n = 365 Loans are different because you pay into the principal when you make a payment, so they are always changing. ( Credit Cards can work the same way if you don’t pay them off. ) Compound Interest n = 4n = 12n=365

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Example: Jasmine has a balance of $685.72 on a credit card that has a 24.9% APR. The interest on this card compounds daily. If she does not charge any money to this account until after she gets her next bill (in 30 days), what will her balance be? B = B = 685.72(1+0.249/365) 30 B = $699.89 Compound Interest 685.72(1+ )0.249/365 365* 30/365

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