Solving Nicaragua's 1988 Inflation Problem

[alyplayford]

Homework Statement

During 1988 Nicaragua's inflation rate averaged 1.3% perd day. This means that on average, prices went up by 1.3 percent from one day to the next. By what percentage did Nicaraguan prices increase in June of 1988? What was Nicaragua's annual inflation rate during 1988?

Homework Equations

I don't understand how to solve this. I know that I need to somehow create a function (I think an exponential function). How would I go about solving this?

The Attempt at a Solution

What I did was figured out how many days from Jan 1, 1988 to May 31, 1988, which is 151. Then I tried to plug that into an exponential format, like this:

P = b(.013)^151

I think that's the wrong direction, and is as far as I got.

 

[Kaimyn]

Are you familiar with compound interest?

If not: $$A=P(1+r)^{n}$$
Where A = the total amount
P = how much you started with
r = the rate as a decimal/fraction
and n = the number of compounding periods

Can you see how this relates to your problem?

And are you sure it's up to June (in the first question), and not just during June? Even if it's not, 1988 is a leap year (which helps with the second question anyway), so there isn't 151 days from January to May.

 

[alyplayford]

After getting help from another person, yes, I understand that you need to use that equation. However, I have no value for P!

So would it look like this:

(1 + .013)^30?

And yes, it's referring only to the month of June, not to the time up to it. That was my mistake.

I got the answer 47.3% for the first part of the problem. Is that right? And how would I solve the second part? Would it be

(1 + .013) ^365

I'm still quite confused.

 

[Kaimyn]

After getting help from another person, yes, I understand that you need to use that equation. However, I have no value for P!

Well, see if you can find what P needs to be if you want the rate. I'll give you a hint:

On the first day, something costing price P now costs 1.013*P
On the second day, something originally costing P now costs 1.013*1.013*P, or about 1.26*P.
You know 1.013 was the original rate, now 1.26 is the rate over two days. In order for this to be true, what does P have to be? (In other words, you don't need P to find the RATE)

I got the answer 47.3% for the first part of the problem. Is that right? And how would I solve the second part? Would it be

(1 + .013) ^365

I'm still quite confused.

Yes, 47.3% is correct, but for the second part, remember that 1988 is a leap year...

 

[alyplayford]

So would it be (1 + .013) ^ 366?