Final answer:
The real interest rate is calculated using the nominal interest rate minus the inflation rate. Given the 14% growth in money stock and 5% growth in real GDP, which totals a 19% inflation rate, the real interest rate would be -8%.
Step-by-step explanation:
To calculate the real interest rate, we need to take into account inflation, which is the general increase in prices and the decline in the purchasing value of money. This can be derived using the Fisher equation, which states that the real interest rate is approximately the nominal interest rate minus the inflation rate. The student's question requires using the quantity theory of money, represented by the equation MV = PY, where M is the money stock, V is the velocity of money, P is the price level, and Y is real GDP. In this case, we are told that the velocity of money is constant, real GDP grows by 5%, and the money stock grows by 14%. As velocity (V) is constant, the change in nominal GDP reflects the change in the money supply plus the change in real GDP, which equals a 19% increase (14% + 5%). The 19% change in nominal GDP is also the inflation rate if the velocity of money is constant. Therefore, to calculate the real interest rate, we subtract this inflation rate from the nominal interest rate.
The formula is as follows:
- Real Interest Rate = Nominal Interest Rate - Inflation Rate
- Real Interest Rate = 11% - 19%
- Real Interest Rate = -8%
Thus, the real interest rate would be -8%, indicating that inflation is eroding the purchasing power of money faster than the nominal interest rate can increase it.