A) Given the following data, calculate the real interest rate for years 2, 3, and 4. (Assume that each CPI number tells us the piece level at the end of each year.)
Year CPI Nominal Interest Rate Real Interest Rate
1 100 --------- --------
2 110 15% ___________
3 120 13% ___________
4 115 8% ___________
b) If you lent $200 to a friend at the beginning of year 2 at the prevailing nominal
interest rate of 15%, and your friend returned the money - with the interest-
at the end of year 2, did you benefit from the deal?
Suppose the required reserve ratio is 0.2. If an extra $20 billion in reserves is injected into the banking system through an open market purchase of bonds, by how much can demand deposits increase? Would your answer be different if the required reserve ratio were 0.1? What would that number be?
Here are your answers.
Let's see what's the general formula to calculate the real interest rate with an example.
At the end of year 1 (beginning of year 2), CPI was 100 and the nominal interest rate was 15%.
If you put $100 in bank, you would have 100*(1+0.15) = $115 at the end of year 2. However, the CPI at the time was 110. This implies that $110 at the end of year 2 bought the same amount of goods that $100 did at the end of year 1. So we must "convert" the $115 to end-of-year-1 dollars. If 110 at the end of year 2 were equivalent to 100 at the end of year 1, then 115 ...
calculate the real interest rate with an example