Future Value of Periodic Savings:
Figuring Out How Much a "Holiday Club" Account Will Contain in the Future:
Note: No use of global variables is permitted in this program. In another words, all variables should be declared inside main or another function.
OBJECTIVE: Practice top-down design, the use of the data type double in mathematical functions, and suitable formatting of the output of double values.
THE ASSIGNMENT: prepare a program which computes the future value of a 'Holiday Club' account.
The idea is that every week, on Friday, a person deposits P dollars into a special savings account. The weekly deposit is always the same: P dollars. Before the first deposit is made, there is no money in the account. Whatever money is in the account earns interest at some specific fixed rate, compounded weekly. As the weeks go by, there is more and more money in the account, and so every week the amount of additional interest is larger and larger. Finally the time arrives for purchasing holiday gifts. One Friday, rather than depositing another payment, the owner of the account withdraws all the money and spends it.
Naturally, people want to know the answers to problems similar to this: "If I put $30.00 in the Holiday Club account per week for 50 weeks, and if the annual interest rate is 9.73%, then how much will be in the account when I withdraw all the money?" This program will answer such problems.
PROGRAM INPUT AND OUTPUT:
The program should start by writing information to describe the purpose of the program, and a general explanation of how to use the program.
The program should then prompt for and input the following three items (in the following order): the amount of the weekly payment, the annual interest rate, and the number of weekly payments. It should print individual prompts for each of the three quantities.
The payment amount should be entered as a fixed-point decimal, denoting dollars and cents, without a dollar sign or commas, by using the decimal point in the standard manner when the amount is not a whole number of dollars. For illustration : the user enters 34.56 to mean 34 dollars and 56 cents, or 100 to mean 100 dollars. The prompt you make for the payment must make such rules clear to the user of the program.
The interest rate should be entered as a fixed-point decimal number of percentage points. For illustration: the user enters 8.125 to mean an annual interest rate of 8.125%. The prompt you create for the interest should make this rule clear to the user of the program.
The number of weekly payments should be entered as a positive integer. For illustration: the user enters 45 to mean forty-five weekly payments. The prompt you create for the number of weekly payments must make this rule clear to the user of the program.
Make sure to prepare the program so that it inputs only:
a) The amount of the payment,
b) The interest rate, and
c) The number of payments,
in that order. If I decide I want to test a program I will want to use redirection from prepared files of input. That won't work out unless you and I have this precise agreement on the form (and order) of the input.
After the user enters the input (payment amount P, interest rate R, and number of weekly payments N), the program must find out the amount of money that will be in the account at the end of N weeks (the future value FV) using this formula:
P((r+1)N - 1)(r+1)
FV = ------------------------
where, r = R/5200, the decimal equivalent of the weekly interest rate.
Of course, the formula above is in a format 'to be understood by humans,' and doesn't have JAVA syntax. Part of your job as programmer is to create suitable JAVA expressions to perform the calculations.
Here is an outlandish illustration of a way to use the formula which may make it more understandable: Assume P is $100 per week, the annual interest rate R is 520% (ten percent per week) and the number of payments N is 2, then r = 520/5200 = 0.10, and
100((1.10)2 - 1)(1.10)
FV = -------------------------------- = $231.00
Another illustration: if P is $100, R is 9.25% and N is 50, then r = 9.25/5200 = 0.001779, and
100((1.001779)50 - 1)(1.001779)
FV = -------------------------------- = $5233.57
Note that your program can use the pow function to compute the power: (r + 1)N
For ex pow(3,2) is 3 to the 2nd power (= 9) and pow(2,5) is 2 two to the fifth power (= 32).
After computing it, the program must prepare a message to standard output (the screen) saying what the future value is. The message must also tell what the input of the user was. For ex, if the user enters 100 for the amount of the payment, 9.25 as the interest rate, and 50 as the number of weeks, then your program should output something very much like this:
The future value of 50 weekly payments of:
$100.00 at 9.250% is $5233.57.
Your program is required to format the numbers for output as shown above.The money should always appear in fixed-point notation, preceded by a dollar sign, and with exactly two digitsdisplayed after the decimal point. The interest rate must be displayed in fixed-point notation, as a percentage, with exactly three digits displayed after decimal point.