Unformatted text preview: ments are made? If the promotion is extended an additional six
years, and no payments are made, what amount would be due?
4. Use Equation 6.2 to show that the time it takes for an investment to double in value does
not depend on the principal P , but rather, depends only on the APR and the number of
compoundings per year. Let n = 12 and with the help of your classmates compute the
doubling time for a variety of rates r. Then look up the Rule of 72 and compare your answers
to what that rule says. If you’re really interested21 in ﬁnancial mathematics, you could also
compare and contrast the Rule of 72 with the Rule of 70 and the Rule of 69.
5. The half-life of the radioactive isotope Carbon-14 is about 5730 years.
(a) Use Equation 6.5 to express the amount of Carbon-14 left from an initial N milligrams
as a function of time t in years.
(b) What percentage of the original amount of Carbon-14 is left after 20,000 years?
(c) If an old wooden tool is found in a cave and the amount of Carbon-14 present in it...
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