Homework 1
Eco 10350, Prin of Macro, Kevin R Foster, Colin Powell School at CCNY
Due 8am Friday Feb 8 
(I think of the deadline as being midnight somewhere on the planet after class, operationalized as 8am EST in NYC on day after)

Each student should submit a separate assignment, even if it is an identical computer file to the rest of your study group. When submitting assignments, please include your name and the assignment number as part of the filename. Please write the names of your study group members at the beginning of your homework.
 
1.	What are the names of the people currently in your study group? (could be null set for now, although I wouldn't advise that to be optimal in long run)
2.	Look at Our World in Data (created by Max Roser) and find the figures on Human Development Index (HDI). Dasgupta, who was writing in 2006, compared the US and Ethiopia. How have those countries done since then? That site has a variety of ways to look at changes over time as well as showing comparisons of HDI with or without GDP. Why do you think that GDP per capita is correlated with the Human Development Index (without GDP)? What countries are relatively wealthy but have a lower HDI? What countries have a better HDI despite lower GDP? How could you characterize those differences?
3.	This question will explore what Dasgupta refers to as the "Rule of 70" (others use "Rule of 72"). Create a spreadsheet with a column for the number of years (beginning at zero and going to 50), another column for the interest rate (begin with R = 3%), and then a column for the value of the investment from an initial amount equal to 1000. At time zero (the top row) the value is the initial amount. At time 1, the value is the initial amount multiplied by (1+R). There are many ways to set up the formulas in the spreadsheet – and this is a good opportunity to learn about something like relative or absolute cell references in your spreadsheet program of choice. (Plan to upload your spreadsheet as part of the homework.)
a.	Using the "Rule of 70", how many years would you guesstimate it would take to double your initial investment at 3%?
b.	With the spreadsheet, what is the value of the investment after that many years again at 3%? Is that the closest to double of any integer value of years?
c.	If interest rate were 5%, what are the values by rule and calculation? At 1%? At what interest rates does the gap between rule of 70 or rule of 72 become significant?
d.	Check that these results on time to double hold for initial investments of 100,000 or 1. Can you show the invariance with a bit of algebra?
e.	John Bogle recently died so we'll calculate the effect of small fees on investment returns. Compare two scenarios: scenario A has interest rate of 6%, scenario B has interest rate of 6% minus 80 basis points (so net 5.2%) paid in fees. How much longer did it take to double your investment? After 10 years, what fraction of your returns went to fees? 
f.	Now we'll check how averaging works (or doesn't). Consider steady scenario C, getting interest of 4% each year, versus choppy scenario D, which goes back-and-forth between 4%+10% and 4%–10% (so 14% and –6%). The average interest rate in scenario D is still 4%, but how does the investment value differ after a few years? 
g.	The Rule of 70 is good for one-time investments but a spreadsheet is better for regular flows. If you invest 100 at year zero, then add 100 more in each subsequent year, then after 15 years you'd have invested 1500 and, at R=3%, have earned how much interest? What if R=7%?
4.	In the OpenStax textbook, please answer the "Problems" at end of Chapter 2, #24, #25, #26, & #27.