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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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Introduction
Compound Interest¶
When you store money at a bank, you can expect that each year you will gain a percent of your holdings as interest. These holdings, however, include any interest earned up until this point which means you earn interest on your interest. This is the idea of compound interest; you will earn more in interest each year as your holdings increase. To illustrate this point, let’s work through an example year by year. Say you start with \$100 in a bank account which gives you an annual rate of 5%. The principal at time 0 is \\$100 which earns 5% interest meaning the principal in time 1 will now be \$150.
In [1]:
p = 100
print("The starting principal is ${}".format(p))
interest = p * .05
print("The interest earned is: ${}".format(interest))
p = p + interest
print("The ending principal is ${}".format(p))
The starting principal is $100
The interest earned is: $5.0
The ending principal is $105.0
Now, the next year we make interest on the $105.
In [2]:
print("The starting principal is ${}".format(p))
interest = p * .05
print("The interest earned is: ${}".format(interest))
p = p + interest
print("The ending principal is ${}".format(p))
The starting principal is $105.0
The interest earned is: $5.25
The ending principal is $110.25
Let's formalize this into a loop to see the effect over the next couple of years.
In [3]:
p = 100
r = .05
for t in range(1,6):
print("----Year {}----".format(t))
print("Starting Principal: ${}".format(p))
interest = p * .05
print("Interest Earned: ${}".format(interest))
p = p + interest
print("Ending Principal: ${}".format(p))
print("---------------")
print()
print()
----Year 1----
Starting Principal: $100
Interest Earned: $5.0
Ending Principal: $105.0
---------------
----Year 2----
Starting Principal: $105.0
Interest Earned: $5.25
Ending Principal: $110.25
---------------
----Year 3----
Starting Principal: $110.25
Interest Earned: $5.5125
Ending Principal: $115.7625
---------------
----Year 4----
Starting Principal: $115.7625
Interest Earned: $5.788125000000001
Ending Principal: $121.550625
---------------
----Year 5----
Starting Principal: $121.550625
Interest Earned: $6.07753125
Ending Principal: $127.62815624999999
---------------
Next
Basics