( Latest Revision: Wednesday Oct 13, 2010 )

THIRD CS 1500 SOLO PROGRAM
Future Value of Periodic Savings

Figuring Out How Much a "Christmas Club" Account Will Contain in the Future

OBJECTIVE:

This assignment is designed to give more practice with top-down design, using doubles in mathematical functions, and doing appropriate formatting of the output of double values.

THE ASSIGNMENT:

Your assignment is to write a program that computes the future value of a "Christmas 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 particular 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. Eventually the time arrives for purchasing Christmas presents. One Friday, instead of depositing another payment, the owner of the account withdraws all the money and spends it on presents.

Naturally, people want to know the answers to questions like this: "If I put 30 dollars in the Christmas club 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 questions.

PROGRAM INPUT AND OUTPUT:

Like many of the example programs we have been reading lately, this program must begin by writing some information explaining the purpose of the program and a general description of how to use the program.

The program must then prompt for and read the amount of the weekly payment, the annual interest rate, and the number of weekly payments (in that same order). It must print individual prompts for each of these three quantities.

The payment amount must be entered as a fixed-point decimal, denoting dollars and cents, without a dollar sign or commas, using the decimal point in the standard manner when the amount is not a whole number of dollars. For example: the user enters 34.56 to mean 34 dollars and 56 cents, or 100 to mean 100 dollars. The prompt you create for the payment must make these rules clear to the user of the program.

The interest rate must be entered as a fixed-point decimal number of percentage points. For example: the user enters 8.125 to mean an annual interest rate of 8.125%. The prompt you create for the interest must make this rule clear to the user of the program.

The number of weekly payments must be entered as a positive integer. For example: 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 write the program so that it inputs only
  1. the amount of the payment,
  2. the interest rate, and
  3. 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 compute the amount of money that will be in the account at the end of N weeks (the future value FV) by using this formula: 


        P((r+1)N - 1)(r+1)
FV =   ------------------------
                  r
(In the formula above, r = R/5200.) For example, if P is 100, R is 520% (ten percent per week) and N is 2, then r = 520/5200 = 0.10, and 

        100((1.10)2 - 1)(1.10)
FV =   --------------------------------   =  $231.00
                 0.10
Another example: 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
                 0.001779
Note that your program can use the pow function to calculate the power: 

         (r + 1)N
For example pow(3,2) is 3 to the 2nd power (=9) and pow(2,5) is 2 two to the fifth power (=32).

After computing the future value, the program will write a message to standard output saying what the future value is. The message must also tell what the input of the user was. For example, 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 paymements of
$100.00 at 9.250% is $5233.57.
Your program is required to format the numbers for output as shown above. The money must always appear in fixed-point notation, preceded by a dollar sign, and with exactly two digits displayed after the decimal point. The interest rate must be displayed in fixed-point notation, as a percentage, with exactly three digits displayed after the decimal point. The "magic formula" on page 56 of Savitch describes the formatting commands you will need in order to get the displays of the output right. Keep in mind that it is the parameter to cout.precision that controls the number of digits after the decmial point.

You can examine a sample script of a program run here.

DESIGN:

I suggest you design the program according to this structure chart. You can write the program by starting with a copy of this program shell. To finish the program using my design suggestion, fill in the definitions of all the functions in the program shell (including "main"). Pay close attention to the header comments for each function. They explain what each function is supposed to do.

You do not have to use my design suggestion or program shell. However, I expect you to employ good principles of top-down design. I will withhold substantial credit if you do not create a program that uses functions appropriately. As my design suggestion illustrates, there are plenty of jobs for individual functions in this program Your program must have at least four functions, including the main function.

DETAILS:

You should put the following lines at the top of your program:: 

#include <cmath>
#include <iostream>

using namespace std ;
WHAT TO TURN IN:

You will be sending me two e-mail messages. Please follow these rules: Here is the list of things you have to turn in: Note that there are no spaces in the subject lines given. It is important that you do not insert any spaces. My e-mail address is:

john@ishi.csustan.edu

WHEN IS THIS ASSIGNMENT DUE?

Look for the due date in the class schedule. (It's at the top level of the class directory.)