Today in Precalculus Turn in graded worksheet Notes: Mathematics of Finance (need a calculator) 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 r= 0.075 =$27,998.18

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

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

Continuously Compound Interest Continuously Compounded interest: A=Pert A: final amount P: principal r: interest rate t: number of years

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

Example 2b t = 30.367 years 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

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

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.

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

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

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

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