Setting
Doubling time is defined as the time it takes for an investment to double. Doubling
time is calculated by using the compound interest formula A 5 Pe^{rt} or
the continuously compounded interest formula A 5 Pe^{rt}. An approximation
to doubling time can be found by dividing 72 by 100r. This approximating technique
is known as the Rule of 72.
Dr. C. G. Bilkins, a nationally known financial guru, has been criticized for
giving false information about doubling time and the Rule of 72 in seminars. Your
team has been hired to provide mathematically correct information for Dr. Bilkins
to use in future seminar presentations.
Tasks
 Evaluating DoublingTime Rules Construct a table of doubling times for interest
rates from 2% to 20% (in increments of 2%) when interest is compounded annually,
semiannually, quarterly, monthly, and daily. Construct a table of doublingtime approximations
for interest rates of 2% through 20% when using the Rule of 72. Devise similar rules
for 71, 70, and 69. Then construct tables for these rules. Examine the tables and
determine the best approximating rule for interest compounded semiannually, quarterly,
monthly, and daily. Justify your choices. For each interest compounding listed above,
compare percent errors when using the Rule of 72 and when using the rule you choose.
Percent error is 100 3 (estimate 2 true value)/(true value). Comment on when the
rules overestimate, when they underestimate, and which is preferable.
 Evaluating the Sensitivity of Doubling Time Dr. Bilkins is interested in knowing
how sensitive doubling time is to changes in interest rates. Estimate rates of change
of doubling times at 2%, 8%, 14%, and 20% when interest is compounded quarterly.
Interpret your answers in a way that would be meaningful to Dr. Bilkins, who knows
nothing about calculus.
Reporting
 Prepare a written report for Dr. Bilkins in which you discuss your results in
Tasks 1 and 2. Be sure to discuss whether Dr. Bilkins should continue to present
the Rule of 72 or present other rules that depend on the number of times interest
is compounded.
 Prepare a document for Dr. Bilkins's speechwriter to insert into the seminar
presentation (which Dr. Bilkins reads from a Teleprompter). It should include (1)
a brief summary of how to estimate doubling time using an approximation rule and
(2) a statement about the error involved in using the approximation. Keep in mind
that Dr. Bilkins wishes to avoid further allegations of misinforming seminar participants.
Also include a brief statement summarizing the sensitivity of doubling time to fluctuations
in interest rates. Include the document in your written report.
 (Optional) Prepare a brief (15minute) presentation of your study. You will be
presenting it to Dr. Bilkins and the speechwriter. Your presentation should be only
a summary, but you need to be prepared to answer any technical questions that may
arise.
