# Math Help - Inflation rate and purchasing power.

1. ## Inflation rate and purchasing power.

Hey guys, I dont understand this questiona and how to do it:

Q. The inflation rate this year is likely to be about 2%. What year will the purchasing power of the dollar be half what it is worth this year if this rate remains constant?

2. Originally Posted by Cockchestner007
Hey guys, I dont understand this questiona and how to do it:

Q. The inflation rate this year is likely to be about 2%. What year will the purchasing power of the dollar be half what it is worth this year if this rate remains constant?
$\displaystyle .50=\frac{1}{1.02^n}$

Solve for n.

3. how do you get .50 and 1.02?? whats the equation beginning equation?

4. Originally Posted by Cockchestner007
how do you get .50 and 1.02?? whats the equation beginning equation?
.50 is half of a dollar.

1.02 = 1 + interest rate

In the first year, it takes 1.02 dollars to buy what cost a dollar last year. Therefore, $\displaystyle\frac{1}{1.02}=.98039$ is the decimal representation of the precent your dollar buys now.

We can write that equation as $\displaystyle .98039=\frac{1}{1.02^1}\Rightarrow x=\frac{1}{1.02^n}$

When is x half of a dollar?

$\displaystyle .50=\frac{1}{1.02^n}$

n is the number of years.

5. Originally Posted by Cockchestner007
how do you get .50 and 1.02?? whats the equation beginning equation?
dwsmith takes 0.5 and 1.02 to be 'half' and '2% increase'.

Can you solve it?

6. yes! thanks so much!

7. A bit like: at 9% annual interest, when will you triple your money?
1.09^n = 3
There is an "unseen" dollar in that formula: 1(1.09^n) = 3 ; when does that dollar become 3 dollars?

8. ## Re: Inflation rate and purchasing power.

For the past couple of years, there has been a ton of dialogue about how Americans are not saving much cash or at least not putting it aside. Even if people were to up the rate of savings, inflation rates have virtually made it an unnecessary exercise.