# How does exchange rate change with respect to interests?

If the central bank raises intereat rates, isn't the money supply now less and the exchange rate is greater? I have run into opposite statements and dont know how to approach this problem. Thanks in advance for everyone's help

• What do you mean when you say, "the exchange rate is greater"? – Art Jan 8 at 6:13
• @Art that a unit of, say, dollars is now worth more pounds – segozcan Jan 8 at 11:24

If by “greater”, you mean higher number It depends on how you quote exchange rate. Under American system the exchange rate between USD and euro would be given by $$S=EUR/USD$$ under European system the exchange rate would be quoted other way around as $$S=USD/EUR$$. So under American system if the USD appreciates due to higher interest rates the $$S$$ would actually get lower while under the European system appreciation would actually lead to greater/higher exchange rate $$S$$.
$$S=ln(p)-ln(p_f)= ln(m)-ln(m_f) -(ln(y)-ln(y_f))+\lambda(i-i_f)$$ (where $$p$$ is price level, $$m$$ money supply, $$y$$, real GDP i interest rate and $$f$$ denotes foreign sector - also I assume that $$ln(L(i)) \approx \lambda i$$so the exchange rate should appreciate when interest rates $$i$$ increases and nothing else change.