# Currency Exchange and Inflation

Question: At a base period, the CPIs of the U.S. and U.K. are both 100, and the exchange rate is \$1.70/GBP. 3 years later, the exchange rate is \$1.60/GBP, and the CPI has risen to 110 in US and 112 in UK. What is the real exchange rate?

I did this using two methods, but I got different answers with each one:

Method 1:

\$new = \$old * 110

£new = £old * 112

Now, \$1.6/GBP after three years means 1 £new = 1 \$new * 1.6

Let’s substitute old values to get the real exchange rate: 1 * (£old * 112) = 1* (\$old * 110) * 1.6

Therefore, 1 £old = (1.6*110/112) * 1 \$old => \$1.5714/£, which is incorrect.

[I do believe the problem lies in \$new = \$old \* 110 and £new = £old \* 112. However, I wrote that equation because if I had bought a candy worth \$1 three years ago, it would be \$1.12 now. I really cannot decipher this.]

Method 2:

GBP has depreciated by : 5.88%; Inflation in GBP has increased by 1.81% relative to USD. Therefore, depreciation of GBP in real terms =~ 5.88% - 1.81% = 4.072%

A million dollar question for me is: What’s wrong with my Method 1? I spent two hours trying to figure out what is it that I am missing. However, I have no clue. I’d appreciate any help.

The problem with method 1 is that you’re incorrectly calculating the new value of each currency.

If the CPI for USD is 110, then:

USD new = USD old ÷ 110

Because it takes 10% more (new) USD to buy the same amount, the value of new USD is _ less than _ the value of old USD.

Similarly, if the CPI for GBP is 112, then:

GBP new = GBP old ÷ 112

Carry on from there.