Morgan: 21.8 Exponential Decay Notes

In class today we worked with a modified version of the compound interest formula and inflation rate to calculate what something would cost in the future adjusted for inflation.

Inflation: A process in which the strenght of the dollar goes down and prices rise as a direct result of this. inflation can be applied to virtually any good (except playstation 3 games apparently).

A = P(1 + r)^n where A = the projected price for something in the future, P = the price of this thing currently, r = the rate of inflation (usually given to you), & n = the number of years that the dollar inflates before you compare it to the earlier value.

This equation is used to find the price of something n years from now.

Example: lets say a hat costs $9.99 presently. we want to know what it will cost 5 years from now. The inflation rate given is 25% annually. You plug in the values to the equation above and you should get your answer

A = $9.99(1 + .25)^5

A = $30.49

The that you buy now for $9.99 will cost $30.49 in 5 years.

Another crucial tool in inflation problems is determining the purchasing power of your dollar in the future. The equation to calculate this is $1/($1 + a) where a = the annual rate of inflation.

Example: lets assume that the annual inflation rate is 25%

$1/($1 + .25) = .80 or %80

This means that in a year you are going to retain only 80% of your purchasing power. You are going to lose 20% of your purchasing power. These numbers are important in the coming equations. trololololololololol. alternatively you could use this equation 1 - ($1/($1 + a)) to go straight to finding how much purchasing power you lose.

The final equation we learned today was A = P(1 - r)^n. This equation is used for determining the value in dollars that something cost n years ago. A = the amount something cost n years ago adjusted for inflation. P = amount something costs currently. r = the deprecation rate (more on this later), n = the amount of years back you want to find the value of something.

Deprecation Rate: is the amount of purchasing power you lose each year. This can be calculated by 1 - ($1/($1 + a))

Example: lets say that you want to buy a car in 2007 & you wonder how much the car would have cost in 2002. The inflation rate has been 25%. The period of time you are looking at is 5 years. In 2007 the car cost $17,400.

1.) Find the deprecation rate:

1 - ($1/($1 + .25)) = .20 OR 20%

2.) Plug swag variables into the deflation equation

A = $17,400(1 - .20)^5

A = $5,701.63

the car would have cost $5,701.63 in 2002 assuming a 25% inflation rate. thats about it for this chapter.

NEXT SCRIBE IS MARK