Transcript Logarithms and Savings Accounts

From week#2 discussion on exponential functions
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Populations tend to growth exponentially not linearly
When an object cools (e.g., a pot of soup on the dinner table), the
temperature decreases exponentially toward the ambient temperature
(the surrounding temperature)
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Radioactive substances decay exponentially
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Bacteria populations grow exponentially
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Money in a savings account with at a fixed rate of interest increases
exponentially
Viruses and even rumors tend to spread exponentially through a
population (at first)
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Anything that doubles, triples, halves over a certain amount of time
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Anything that increases or decreases by a percent
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Remember that exponential equations are in the
form:
y = P(1+r)x
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P is the initial (reference, old) value
r is the rate, a.k.a. percent change (and it can be
either positive or negative)
x is time (years, minutes, hours, seconds
decades etc…)
Y is the new value
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Applying exponential formula to saving account
applications…
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Putting your money into a savings account is
like loaning the bank your money
Buying savings bonds you actually loan money
to the government
In return the bank/government pays you
interest…
And gets to use your savings to generate more
money
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Through investments, loans, etc…
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The amount of interest you are paid for loaning
your money
Formula for calculating APR is
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A=P*(1+r/n)^(nY)
 P = beginning balance
 r = annual interest rate
 n = compounding frequency (1=annually, 4 = quarterly,
12 = monthly)
 Y = number of years
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You deposit $800 into a savings account that
has and annual percentage rate of 2.1%
compounded quarterly.
What is your balance after the first year?
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A=P*(1+r/n)^nY)
A=800*(1+.021/4)^(4*1)
A=$816.93
What is your balance after 5 years?
How long would it take your money to double?
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Hint: Use logs
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Use the percentage increase/decrease formula
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In this case Y=P*(1+r)^x
The equation?
1600 = 800*(1+.021/4)^4x
 Divide by 800
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2 = (1.00525)^4x
 Take log of both side
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Log 2 = log(1.00525)^4x
 Follow rule #2
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Log 2= 4x* log(1.00525)
 Divide by log(1.00525)
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33.35 years to double your money
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Percentage rate reflecting the total interest to be
earned based on:
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the interest rate
an institution’s compounding method
assuming funds remain in account for a 365-day
year.
Formula
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Use Percentage change formula for 2 consecutive
years
=(new-old)/old
Change value to a %, show 2 decimal places
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Check out this link
ABC's of Figuring Interest