HOW do you get this answer?

Question

I am stuck on this problem even as simple as it may seem. The problem is:

If the price level increases 20%, the purchasing power of money decreases by what percentage?

answer: 16.67%

The equation the book gives me is V = 1/P, where V is the purchasing power and P is the price level.

I have tried V = 1/1.2 but I only get 0.83

Answer 1

Let's say that you have $\$1.00$. The thing that you had planned to buy that yesterday cost $\$1.00$ now costs $\$1.20$. So you can only buy $\frac56$ of the thing. Thus you have lost $\frac16$ of your purchasing power, or $16 \frac23 \%$