Java Reference
In-Depth Information
5.
You have just purchased a stereo system that cost $1,000 on the following
credit plan: no down payment, an interest rate of 18% per year (and hence
1.5% per month), and monthly payments of $50. The monthly payment of
$50 is used to pay the interest, and whatever is left is used to pay part of the
remaining debt. Hence, the first month you pay 1.5% of $1,000 in interest.
That is $15 in interest. So, the remaining $35 is deducted from your debt,
which leaves you with a debt of $965.00. The next month, you pay interest
of 1.5% of $965.00, which is $14.48. Hence, you can deduct $35.52 (which is
$50 - $14.48) from the amount you owe. Write a program that tells you how
many months it will take you to pay off the loan, as well as the total amount
of interest paid over the life of the loan. Use a loop to calculate the amount
of interest and the size of the debt after each month. (Your final program need
not output the monthly amount of interest paid and remaining debt, but you
may want to write a preliminary version of the program that does output these
values.) Use a variable to count the number of loop iterations and hence the
number of months until the debt is zero. You may want to use other variables
as well. The last payment may be less than $50 if the debt is small, but do not
forget the interest. If you owe $50, your monthly payment of $50 will not pay
off your debt, although it will come close. One month's interest on $50 is only
75 cents.
6.
The Fibonacci numbers F n are defined as follows: F 0 is 1, F 1 is 1, and
F i+2 = F i + F i+1
i = 0, 1, 2, . . . . In other words, each number is the sum of the previous two
numbers. The first few Fibonacci numbers are 1, 1, 2, 3, 5, and 8. One place
where these numbers occur is as certain population growth rates. If a population
has no deaths, then the series shows the size of the population after each time
period. It takes an organism two time periods to mature to reproducing age, and
then the organism reproduces once every time period. The formula applies most
straightforwardly to asexual reproduction at a rate of one offspring per time
period. In any event, the green crud population grows at this rate and has a time
period of 5 days. Hence, if a green crud population starts out as 10 pounds of
crud, then in 5 days, there is still 10 pounds of crud; in 10 days, there is 20
pounds of crud; in 15 days, 30 pounds; in 20 days, 50 pounds; and so forth.
Write a program that takes both the initial size of a green crud population (in
pounds) and a number of days as input and outputs the number of pounds of
green crud after that many days. Assume that the population size is the same for
4 days and then increases every fifth day. Your program should allow the user to
repeat this calculation as often as desired.
The value e x can be approximated by the sum:
7.
1 + x + x 2 /2! + x 3 /3! + . . . + x n / n !
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