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The figure in the New York Times article “Trading Stocks for Bonds Poses Its Own
Risks” is shown below.
Compound Interest Formula
The amount 𝐴 after 𝑡 years due to a principal 𝑃 invested at an annual interest rate 𝑟
compounded 𝑛 times per year is
𝐴 = 𝑃 (1 +
𝑟
𝑛
)
𝑛𝑡
According to the New York Times article, “a typical portfolio of stocks might earn 7
percent on average, compared with the 1.55 percent yield of a long-term bond these
days.” Using the compound interest formula, with a principal of 25,000 and annual
compounding, the amount for stocks and bonds, denoted by 𝐴𝑠 and 𝐴𝑏, respectively, are
𝐴𝑠 = 25000(1 + 0.07)
𝑡
𝐴𝑏 = 25000(1 + 0.0155)
𝑡

Problems

1. What is the difference between linear growth and exponential growth?
2. What is the nominal value of the stock portfolio after 40 years?
3. What is the nominal value of the bond portfolio after 40 years?
4. Use Maple to plot 𝐴𝑠 and 𝐴𝑏 for 𝑡 from 0 to 40. (Hints can be found in the
   appendix.)
5. Assuming a 3 percent inflation rate, the adjusted amounts are
   𝐴𝑠 = 25000[1 + (0.07 − 0.03)]
   𝑡
   𝐴𝑏 = 25000[1 + (0.0155 − 0.03)]
   𝑡
   Repeat Problems 2, 3, and 4 with the inflation adjusted formulas.
6. (Extra) Repeat Problem 5, using the current projected annual rate of inflation for
   the U.S. State how you obtain the inflation rate.
   Report
   Incorporate your answers the above problems into an essay. Please be sure to include the
   following elements.
7. In your own words state the issue you were inquiring. (Recall, you were to
   investigate the investment options of stocks versus bonds. Re-read the New York
   Times article to refresh your memory.)
8. Clearly state how you obtain relevant numerical information, such as the average
   return rate of stocks, the interest rate, and the inflation rate.
9. Show your calculations (you may take a picture of your hand calculations, and
   insert it into your document). It’s important to show your Maple work, including
   the graphs.
10. Write a conclusion. Use your graphs and calculations to describe the pros and
    cons about investing in stocks versus bonds.
11. Ensure clear citations for information you obtain from the internet or print
    publications. Visit https://library.laguardia.edu/research/apa for the APA
    (American Psychological Association) style guide. You may consult a librarian
    for help with your citations.
    Reference
    Wasik, John E. (2016, August 27). Trading Stocks for Bonds Poses Its Own Risks. The
    New York Times, p. B4.
    Appendix

restart:
As := t -> 25000(1+0.07)^t; Ab := t -> 25000(1+0.0155)^t;
plot([As(t), Ab(t)], t=0..40, title = “Return of a
$25,000 investment over 40 years”, legend = [“Stock”,
“Bond”]);
As(40);
Ab(40);

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