Economics And Interest Rates?

I’m having a very hard time with these questions can you look what i have over and tell me what you think? I’m not exactly sure what good answers are to some of these. all help would be greatly appreciated
2. (50 POINTS total) Another important real economic variable we consider in this homework assignment is the real interest rate. We learned that the real interest rate is the difference between nominal interest rates and inflation. In fact, there are two real interest rates: ex-ante and ex-post. Ex-ante real interest rates are the expected real rates where ex-post real interest rates are the real rates that were actually realized. An example is in order. Suppose one year nominal interest rates are 5% and you expect that prices are going to rise by 3% (i.e., your expected rate of inflation (πe) is 3%). Your ex-ante or expected real rate of interest is therefore 2%. Now suppose that over the year inflation wasn’t 3% but 4% instead (your expectation was wrong). That is, actual inflation (π) equaled 4% and thus your actual real rate, referred to as the ex-post real rate of interest is only 1%. Naturally, ex-ante and ex-post real interest rates differ anytime your expectations of inflation are wrong. To summarize, the ex-ante real rate is equal to i – πe where the ex-post real rate is equal to i – π. In general, it is the ex-ante rate that is most important since we never really know what the inflation rate is going to be so we have to guess and that is the all important expected inflation term (πe).
In parts a) and b) we use real data again and since we really don’t have information on inflationary expectations we will be using actual inflation and therefore working with ex-post real rates.
Please use the following data from FRED
CPI Price index (P) use CPIAUCSL
Nominal one year rates (i) GS1
a) Calculate the real rate of interest (ex-post) for the first year of the last 4 decades. In particular, calculate the real rate of interest from 1970 – 1971, 1980 – 1981, 1990 – 1991, and 2000 – 2001. Use the one year nominal rate in January of 1970, 1980, 1990, and 2000 (we are considering whether we should save for a year or spend!) and calculate the rate of inflation from Jan 1970 to Jan 1971, Jan 1980 to Jan 1981, Jan 1990 to Jan 1991, Jan 2000 to Jan 2001. Show all work including your calculation of inflation (using price indexes).
i70=8.1 i71=4.57 i80=12.06 i81=14.08 i…
i00=6.12 i01=4.81
PI70=37.9 PI71=39.9 PI80=78 PI81=87.2 …
PI00=169.3 PI01=175.6
π70 = [(39.9-37.9)/37.9]*100 = 5.28% π80 = [(87.2-78)/78]*100 = 11.79%
π90 = [(134.7-127.5)/127.5]*100 = 5.65% π00 = [(175.6-169.3)/169.3]*100 = 3.72%
r70 = 8.1 – 5.28 = 2.82 r80 = 12.06 – 11.79 = .27 r90 = 7.92 – 5.65 = 2.27
r00 = 6.12– 3.72 = 2.4
b) Using your answer in part a) above, when would it have been best to save and when would it have been best to spend (consume), all else constant? Explain.
It would have been best to consume in 80-81, 90-91, and 2000-01 because the real interest rate was positive meaning the same nominal amount of money would be worth less in the future but in 70-71 the real interest rate was negative meaning the same nominal amount would be worth more the next year giving people reason to save and hold onto their cash
c) Suppose we decided to save one year ago and purchased a one year bond in July of 2009. We cashed it in at the end of July, 2010. What was the nominal rate of interest, the rate of inflation (or deflation) and the ex-post real interest rate?
d) Ex-ante, that is, when we purchased the bond in July of 2009, our expected rate of inflation was 2% because that is what Ben Bernanke told us his inflation target was. What is the ex-ante real rate of interest and why does it differ from the ex-post real interest rate?
e) We discussed the evils of deflation in a central banking context. Why exactly is deflation a nightmare for central bankers? How can Central Bankers make sure they avoid the nightmare? Use the Fisher equation throughout and be very specific as to the ‘nightmare.’
The Nightmare of deflation is that when deflation occurs the money people have gains value this means people are much more likely to save and less likely to borrow money when you would have to pay the loan back with dollars that are now worth more. What it really comes down to is that the real interest rate as seen in the Fisher equation becomes negative. When the Real interest rate is negative and deflation occurs the economy will become stagnant.
Central Bankers have 1 real tool to avoid deflation, they manipulate the nominal interest rate to keep