Please help with solving the following (*Be detailed and thorough) :

6. You are considering the choice between investing $50,000 in a conventional 1-year bank CD offering an interest rate of 5% and a 1-year "Inflation-Plus" CD offering 1.5% per year plus the rate of inflation.

a. Which is the safer investment?

b. Can you tell which offers the higher expected return?

c. If you expect the rate of inflation to be 3% over the next year, which is the better investment? Why?

d. If we observe a risk-free nominal interest rate of 5% per year and a risk-free real rate of 1.5% on inflation- indexed bonds, can we infer that the market's expected rate of inflation is 3.5% per year?

7. Suppose your expectations regarding the stock price are as follows:

State of the Market	Probability	Ending Price	HPR (including dividends)
Boom	0.35	$140	44.5%
Normal growth	0.30	110	14.0
Recession	0.35	80	16.5

Use Equations 5.11 and 5.12 to compute the mean and standard deviation of the HPR on stocks.

8. Derive the probability distribution of the 1-year HPR on a 30-year U.S. Treasury bond with an 8% coupon if it is currently selling at par and the probability distribution of its yield to maturity a year from now is as follows:

State of the Economy	Probability	YTM
Boom	0.20	11.0%
Normal growth	0.50	8.0
Recession	0.30	7.0

For simplicity, assume the entire 8% coupon is paid at the end of the year rather than every 6 months.

13. During a period of severe inflation, a bond offered a nominal HPR of 80% per year. The inflation rate was 70% per year.

a. What was the real HPR on the bond over the year?

b. Compare this real HPR to the approximation rreal rnom i.

Homework problems reproduced from the course textbook: Bodie, Z., Kane, A., & Marcus, A. J. (2021). Investments (12th ed). New York, NY: McGraw-Hill Education. ISBN: 978-1-260-01383-2.