what is the general formula for figuring out this question?

If the dinar devalues against the US dollar by 45%, the US dollar will appreciate against the dinar by...?

I'm not getting this at all, and the book is not helping!!

Use simple algebra, and start with an example. Say, initially, 1 dinar = 1 dollar. Then the dinar devalues by 45% so that 1 dinar = .65 dollar. With this, how many dinar's is 1 dollar. Well 1 dollar / .65 = 1.54. So, the dollar appreciated against the dinar by 54%.

oops, sorry stupid mistake. if the dinar devalues by 45% that means 1 dinar = .55 dollars. Take it from here.

The answer above is wrong. the correct answer is 82%

To figure out how much the US dollar will appreciate against the dinar, you can use the following general formula:

Appreciation (%) = Devaluation (%) / (1 - Devaluation (%))

In this case, the given devaluation is 45%. So, you can plug in this value into the formula to calculate the appreciation:

Appreciation (%) = 45% / (1 - 45%)

To simplify the calculation, you need to convert the percentages into decimals by dividing them by 100:

Appreciation (%) = 0.45 / (1 - 0.45)

Now, let's calculate the result:

Appreciation (%) = 0.45 / 0.55

Appreciation (%) ≈ 0.8182

So, if the dinar devalues against the US dollar by 45%, the US dollar will appreciate against the dinar by approximately 81.82%.

I hope this clears things up for you!