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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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Basics
While you can loop through every year to determine the ending value, there is also a simple formula which can calculate at each point in time what the value of the account should be. This formula is:
$ A = P * (1+r)^t $
where
$ A = \text{Ending value of the account} $
$ P = \text{Starting principal of the account} $
$ r = \text{Annual rate of return} $
$ t = \text{Number of years} $
In [4]:
p = 100
r = .05
for t in range(1,6):
A = p * (1+r) ** t
print("----Year {}----".format(t))
print("Ending Principal: ${}".format(A))
print("---------------")
print()
print()
----Year 1----
Ending Principal: $105.0
---------------
----Year 2----
Ending Principal: $110.25
---------------
----Year 3----
Ending Principal: $115.76250000000002
---------------
----Year 4----
Ending Principal: $121.55062500000003
---------------
----Year 5----
Ending Principal: $127.62815625000003
---------------
To make our life easy, let's create a function that will compute the future value of an investment and then check to make sure it works.
In [5]:
def compoundInterest(p,r,t):
A = p*(1+r)**t
return A
p = 100
r = .05
for t in range(1,6):
A = compoundInterest(p,r,t)
print("----Year {}----".format(t))
print("Ending Principal: ${}".format(A))
print("---------------")
print()
print()
----Year 1----
Ending Principal: $105.0
---------------
----Year 2----
Ending Principal: $110.25
---------------
----Year 3----
Ending Principal: $115.76250000000002
---------------
----Year 4----
Ending Principal: $121.55062500000003
---------------
----Year 5----
Ending Principal: $127.62815625000003
---------------
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