What does an increase in the aggregate price do?

What are some reasons that would cause interest rates to increase but the price level to also increase?

• I'm doing a research assignment into whether an increase in interest rates causes a decrease in the price level (CPI) as expected using real market data. There are some quarters where interest rates increase but the price level increases, and others where interest rates decrease but the price level also decreases. What are some factors not accounted for in the theoretical relationship that could cause these things to happen?

• Answer:

  Oil price shock: Sudden increase in oil price will lead to firms increasing their mark up. As a result price level (inflation) increase. As price level increase, it means real money supply decrease. Real money supply = money supply divided by price level (MS/P). Therefore, a decrease in money supply will lead to the LM curve shifting to the left. As LM shift to the left interest rate increase. So it is possible to have both increasing at the same time. Hope this helps.