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L22_blanks - Day 27 Lecture 22 Non-Linear Models The Final...

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1 Day 27 Lecture 22 Non-Linear Models, The Final Chapter Stuff I should have just stated instead of Derived… Example Version If a Bank offers 3% APR , and the bank compounds twice a year, then the interest payment each compound period is 1.5% of the current amount of money in the account. Theoretical Version If a Bank offers APR , and the bank compounds times a year, then the interest payment each compound period is of the current amount in the account The relationship between the Annual Percentage Rate, , and the Compound Period Interest rate is… 2 1
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2 Where’s my money? This is actually a good thing since later installments will actually pay interest on previously gained interest before the year is up. Using the Generic Compound interest formula, we can derive a formula for the amount in terms of ___________. Suppose years have passed, then… 3 11 # of Comp. Per. after Investing 0 1 2 = 1 Yr 3 4 = 2 Yr Amountin the Account Interest paid at the E.O.C.P 200 203 3 206.04… 3.04… 206.04… 209.13… 3.09… 206.04… 209.13… 212.27… 3.13… 3.18… One is never enough… What if the banks wants to offer compounding more than twice a year? There’s a formula for that! Using the generic Compound Interest formula we see that represent the amount in an account years after opening if interest is compounded times per year. 4 4
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3 So many Options to Choose from, part 1 Banks can offer Compounding Annually: Semi-Annually: Bi-monthly 5 0 # of Years since Investing 0 1 2 3 4 Amountin the Account 200 206 212.18 218.55 225.10 Interest paid at the E.O.Y 6 6.18 6.37 6.55 # of Years since Investing 0 1 2 3 4 Amountin the Account 200 206.05 212.27 218.69 225.30 Interest paid at the E.O.Y 6.05 6.23 6.42 6.61 # of Years since Investing 0 1 2 3 4 Amountin the Account 200 206.08 212.34 218.79 225.43 Interest paid at the E.O.Y 6.08 6.26 6.45 6.65 So many Options to Choose from, part 2 And they can also offer... Monthly: Weekly: Dailey: 6 0 # of Years since Investing 0 1 2 3 4 Amountin the Account 200 206.08 212.35 218.81 225.47 Interest paid at the E.O.Y 6.08 6.27 6.46 6.66 # of Years since Investing 0 1 2 3 4 Amountin the Account 200 206.09 212.36 218.83 225.49 Interest paid at the E.O.Y 6.09 6.27 6.47 6.66 # of Years since Investing 0 1 2 3 4 Amountin the Account 200 206.09 212.37 218.83 225.50 Interest paid at the E.O.Y 6.09 6.28 6.47 6.66
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