G.21 Write a short paper about Fibonacci numbers. You might check The Fibonacci Quarterly, particularly "A Primer on the Fibonacci Sequence," Parts I and II, in the February and April 1963 issues. The articles, written by Verner Hogatt and S. L. Basin, are considered classic articles on the subject. One member of your group should investigate the relationship of the Fibonacci numbers to nature, another the algebraic properties of the sequence, and another the history of the sequence.

G.22 Suppose you were hired for a job paying $21,000 per year and were given the following options:

OPTION A: Annual salary increase of $1,200
OPTION B: Semiannual salary increase of $300
OPTION C: Quarterly salary increase of $75
OPTION D: Monthly salary increase of $10

Each person should write the arithmetic series for the total amountofmoneyearnedin10 years under a different option.

Your group should reach a consensus as to which is the best option. Give reasons and show your calculations in the paper that your group submits.

G.23 It is not uncommon for the owner of a home to receive a letter similar

to the one shown below. Write a paper based on this letter. Different members of your group can work on different parts of the question, but you should submit one paper from your group.

a. What is the letter about?

A computer printout (above) was included with the letter. Assuming that these calculations are correct, discuss the advantages or disadvantages of accepting this offer.

c. The plan as described in the letter costs $375 to sign up. I called the company and asked what their plan would do that I could not do myself by simply making 13 payments a year to my mortgage holder. The answer I received was that the plan would do nothing more, but the reason people do sign up is because they do not have the self-discipline to make the midmonthly payments to themselves. Why is a biweekly payment equivalent to 13 annual payments instead of equivalent to a monthly payment?

d. The representative of the company told me that more than 250,000 people have signed up. How much income has the company received from this offer?

e.You calculated the income the company has received from this offer in part d, but that is not all it receives. It acts as a bonded and secure "holding company" for your funds (because the mortgage company does not accept "two-week" payments). This means that the

company receives the use (interest value) on your money for two weeks out of every month. This is equivalent to half the year. Let's assume that the average monthly payment is $1,000 and that the company has 250,000 payments that they hold for half the year. If the interest rate is 5% (a secure guaranteed rate), how much potential interest can be received by this company?