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Compound Interest Part 1 6
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IntroductionLecture1.1
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Basics 30 minLecture1.2
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Plotting Compound InterestLecture1.3
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Plotting Compound Interest Part 2Lecture1.4
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Comparing rLecture1.5
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More PlottingLecture1.6
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Compound Interest Part 2 3
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Changing rLecture2.1
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Interest with WithdrawalsLecture2.2
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Effective Interest RateLecture2.3
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Present Value 4
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Plotting CashflowsLecture3.1
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Present ValueLecture3.2
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Present Value Part 2Lecture3.3
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Multiple CashflowsLecture3.4
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Annuities 6
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IntroductionLecture4.1
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Annuity EquationLecture4.2
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Annuity DiscountingLecture4.3
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Annuity DueLecture4.4
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Semi-annual RateLecture4.5
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Annuities ConclusionLecture4.6
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Perpetuities 2
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IntroductionLecture5.1
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PerpetuitiesLecture5.2
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Bonds 6
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IntroductionLecture6.1
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Bond ValuationLecture6.2
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Discount BondLecture6.3
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Par BondLecture6.4
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Premium BondLecture6.5
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Finding rLecture6.6
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Dividend Discount Model 3
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IntroductionLecture7.1
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Dividend Discount ModelLecture7.2
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Dividend Discount Model Part 2Lecture7.3
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Risk 8
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IntroductionLecture8.1
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Market ReturnsLecture8.2
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Market RiskLecture8.3
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CovarianceLecture8.4
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Graphing Market ReturnsLecture8.5
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Correlation and BetaLecture8.6
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Creating PortfoliosLecture8.7
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DiversificationLecture8.8
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Capital Asset Pricing Model 6
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IntroductionLecture9.1
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CAPM InputsLecture9.2
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Comparing CAPMLecture9.3
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CAPM PortfoliosLecture9.4
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Shorting a StockLecture9.5
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AlphaLecture9.6
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Finding r
Finding r¶
To find r we are going to have a much tougher time since there is no easy equation solution. To solve it we need to experiment. Let’s set the parameters below and try out different values of r and see if it will get us to match the values. In this lesson we are going to just try a couple values, but there are more advanced methods that you can use that we won’t introduce here. I made the example easy to work out by guessing very 1% within a limited range.
#Set up the parameters
PV = 768.3479521244554
F = 1000
c = .02
n = 10
We can predict the present value for something like say 2% and see what the difference between the actual and predicted is.
#Let's try to see what our PV would be if r=2%
predicted = bond_value(F,c,n,.02)
print(predicted)
1000.0
If we check the difference we see it is not very close.
print(predicted-PV)
231.65204787554455
What we could do is test different rates and see which one gets us closest to the PV we are given
rates = [x/100 for x in range(1,13)]
print(rates)
print()
values = [bond_value(F,c,n,x) for x in rates]
print(values)
[0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.1, 0.11, 0.12]
[1094.7130453070167, 1000.0, 914.6979716322417, 837.7820844128994, 768.3479521244554, 705.596517943412, 648.8209229533697, 597.3951160635131, 550.7639609188691, 508.4346315436251, 469.9691189972911, 434.97769715891326]
If we look for the absolute value in the difference between present value and predicted, this will help us find the closest fit.
#Differences
diff = [abs(x-PV) for x in values]
print(diff)
[326.3650931825613, 231.65204787554455, 146.35001950778621, 69.43413228844395, 0.0, 62.751434181043464, 119.5270291710857, 170.95283606094233, 217.58399120558636, 259.9133205808304, 298.37883312716434, 333.3702549655422]
#Find the the minimum error
print(min(diff))
0.0
#Get the index of it
i = diff.index(min(diff))
print(i)
4
#And find the rate that got us there
print(rates[i])
0.05
After doing this, we see that we have the correct rate r to get the present value we saw before!
print(PV)
print(bond_value(FV,cr,n,rates[i]))
768.3479521244554
768.3479521244554