1. You earned a 7.1% nominal rate of return on your investments over the past year. But at the same time, the reported inflation rate was 3.1%. What was your real rate of return for the year (the percentage increase in your real wealth)? Enter answer as percents, accurate to 2 decimal places.
2. You want to make an average rate of return of 8.2% on your money. An acquaintance approaches you for a one-year loan. You think he's a pretty decent fellow, but estimate that there's a 1.9 % chance that the guy will pull a runner and you get nothing back. There's a further 3.2 % chance that he will cite 'financial difficulties' and only pay back 50% of the money owed. If that's the case, what interest rate must you charge him in order to make your desired rate of return in expectation? Enter answer in percents, accurate to 2 decimal places.
3. You invest $870 at 7% per year, and are waiting for it to grow to $9,072. How many years will you have to wait?
4. You want to have $1 million in your investment account in 18 years, and estimate that you ran earn an 6% rate of return. How much do you need to invest today (assuming you make no further contributions), in order to achieve your goal?
5. Assume your utility function is the cube root. If your current total wealth is 16.1 thousand dollars, what is the marginal utility of the next 500 dollars you will make?