Charlie Krampf
Professor Little
Applied PreCalculous
April 11th, 2014
Compounded investments, and interest rates
Formulas
1) A=P(1+r)^t - compounded once a year
2) A=P(1+r/n)^n*t - compounded in a year, monthly, weekly, daily
3) A=Pe^rt - compounded continuously
Purpose
- Used for investments and telling how revenue an investment will put out. These formulas are extremely important, because how commonly they are used.
- In my mind these formulas are an absolute necessity for people to know.
Understanding Variables
A = future Amount
P = Initial Amount
R = Interest Rate
T = Number of years
N = compounded in one year: monthly (12) Weekly (52) Daily (365)
e = 2.71
Understanding Usage
- It is mainly used to help with financing, and finding out revenue growth on investments. Investments ranging from federal bonds to penny stocks on the NYSE (New York Stock Exchange)
- It can also be used to find the estimate of growing population. Such as the population of a town, or city.
Using each Formula
Formula (1) is used when your investment is only compounded on a yearly bases.
Ex. lets say you invest $5000 into a bank that has an interest rate 5% for 12 years.
P= $5000
r= 5% to find the percent divide 5/100, this equals .05
t= 12
A=5000(1.05)^12
A= $8979.28
Formula (2) is used when your investment is compounded during one year, this is why the variable,n, is in this equation.
Ex. Same numbers as example number except this formula will be compounded monthly
P=$5000
r=5% = .05
t=12
n=monthly = 12
A=5000(1.0041)^12*12
A=$9012.66
- The more an investment is compounded the higher the yield it will have the investor.
Formula (3) is used when an investment is continuously compounded. Since this investment is continuously compounded will it be yield more or less then the other two formula’s?
Ex. Again, the same numbers used before.
P=$5000
r=5% = .05
t=12
e=2.17
A=5000e^.05*12
A=$9110.59
Population Example
Lets say the city of Boston has 10,000 residents and the population is growing at a 12% rate on a yearly bases.
P=10,000
r= 12% = .12
t= 1
A=10,000(1.12)^1
A=11,200
Now, lets say the city has 10,000 residents and a population growth of 6% each day for ten years
P=10,000
r=6% = .06
t=10
n=365
A=10,000(1+.12/365)^.12*365
A=10,000(1.00016)^4380
A=20,153
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If you have had any trouble understanding this please check out this Khan Academy Link
very well organized post, especially with the "purpose," "understanding variables," and "understanding usage" along with your examples the whole concept is explained thoroughly and concisely.
ReplyDeleteCharlie, I think this is a great post! The layout is very easy to follow, and you very clearly define all of the terms. Good job!
ReplyDeletecharlie,
ReplyDeletegreat job! and good job of including a real world example with the population growth. =0]
professor little