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Today in Precalculus

Today in Precalculus. Notes: Mathematics of Finance Interest rates Annual Percentage Yield Homework. Compound Interest. Compound interest:. A: final amount P: principal r: interest rate k: number of payments per year t: number of years. Example 1. P=$18,000 k = 2 t = 6

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Today in Precalculus

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  1. Today in Precalculus • Notes: Mathematics of Finance • Interest rates • Annual Percentage Yield • Homework

  2. Compound Interest • Compound interest: A: final amount P: principal r: interest rate k: number of payments per year t: number of years

  3. Example 1 P=$18,000 k = 2 t = 6 r= 0.075 =$27,998.18

  4. P=$18,000 k = 4 t = ? r= 0.075 A=$27,000 27,000=18,000(1.01875)4t 1.5=1.018754t log1.5 = 4tlog1.01875 4t=21.827 t = 5.457 years Example 1b

  5. Example 1c A=$31,500 P=$18,000 k = 12 t = 15 r= ? r= .0374 So an interest rate of 3.74% is required.

  6. ContinuouslyCompound Interest • Continuously Compounded interest: A=Pert A: final amount P: principal r: interest rate t: number of years

  7. Example 2 P=20,000 t = 8 r = 0.053 A=20,000e(8•.053) = $30,561.23

  8. Example 2b 100,000 = 20,000e.053t 5 = e0.053t ln5 = 0.053t A = $100,000 P = $20,000 r = 0.053 t = ? t = 30.367 years

  9. Example 2c A = $40,000 P = $20,000 r = ? t = 10 40,000 = 20,000e10r 2 = e10r ln2=10r r =.0693 An interest rate of 6.93% is needed

  10. Annual Percentage Yield (APY) • A common basis for comparing investments with different interest rates and methods of compounding. • The percentage rate that, if compounded annually, would yield the same return as the given interest rate with the given compounding.

  11. Example 1 Bob invests with the local bank at 2.12% interest compounded monthly. What is the equivalent APY? So the APY is 2.14%. This means his investment compounded monthly at 2.12% earns the same interest as if it earned 2.14%, compounded once a year. =.0214

  12. Which investment is more attractive, one that pays 8.5% compounded quarterly or another that pays 8.45% compounded monthly? x=.0877 Example 2 x=.0879 So the investment with the 8.45% rate compounded monthly is the better investment

  13. Example 3 The interest charge by your credit card company is 18.75% APY. What is the monthly interest charge on a balance of $5,000? r= .1731 $5000x.1731 = $865.43

  14. Homework • Pg 341: 3-9 odd, 21-39odd, 41-46all

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