# The following formula will compute the Total Amount

The following formula will compute the Total Amount that will be accumulated for a given

Monthly Amount saved:

Notice that his formula also requires that you first calculate a factor and then use it in your

formula. The factor formula is:

factor = exp( numberOfMonths * log(1 + monthlyInterestRate))

exp and log are predefined mathematical functions, located in the C++ library.

For hand calculating results to test your program, the equivalent algebraic equation is:

factor = (1 + monthlyInterestRate) numberOfMonths

Write a program to output accumulated values for each month, given a set amount saved each

month, until the accumulated amount reaches a set goal amount.

Discussion about comparing floating point values:

Given two floating point values:

num = 9.99999999

num2 = 10.00000000

If both are displayed to two decimal places, you will see:

10.00 and 10.00

However, if you compare the same two values within your code, to see if they are equal, the

comparison test will be false (i.e. they are not equal).

This can cause problems for programs that compare floating point values.

But we can fix this problem by forcing the stored value to be rounded to 2 decimal places (not

just the output value).

The formula:

num = floor((num * 100) + 0.5) / 100.0;

will change the value stored in num to be:

num = 10.00000000

And then if you compare num with num2, they will be found to be equal.

Requirements:

Ensure that you define constants for all fixed values. After defining the constants:

– Use only the constant name in your code (no hardcoded constant values).

– The usage of only constant names includes references in the executable code, the

prompts and error messages, and the comments — no hardcoded values anywhere!

Use the double data type for all floating point values.

The program should:

. Tell the user what the program does before prompting for input.

. Read from the user the amount that will be saved each month.

o The user must enter a value between $5 and $5000 inclusive. If they do not, issue

an error message and then re-prompt the user to enter the number again, until a

valid value is entered.

. Read from the user the annual interest rate.

o The user must enter a value between 1% and 25% inclusive. If they do not, issue

an error message and then re-prompt the user to enter the number again, until a

valid value is entered.

o After reading a valid value, the program will need to convert the annual interest

rate to a monthly interest rate (divide by 100 to get a fractional interest rate, and

then divide that by 12 for monthly interest) before using it in the formulas.

. Read from the user the goal amount they wish to reach.

o The user must enter a positive amount of no more than $ 999,999.99 (i.e. under 1

million). If they do not, issue an error message and then re-prompt the user to

enter the number again, until a valid value is entered.

. Determine the factor and the total amount accumulated as calls to two different user-

defined functions.

o The first function will return the factor for a specific number of months.

o The second function will return the total amount accumulated for a specific

number of months

o Pass any required information, including the number of months to calculate the

value for, to the functions as parameters.

. Display the month number and the total amount accumulated, for every month until

the goal is reached, formatted as shown in the output example below.

o NOTE: Use the rounding formula provided above to round the value returned

from the function and stored in the total amount accumulated variable to 2

decimal places, before comparing it to any other value.

. The program should cease displaying these values as soon as the total amount

accumulated is at or above the goal.

. After the goal has been reached, display the annual interest rate, savings per month, total

number of months, and final amount accumulated formatted as shown in the output

example below.

Sample Input

Program will calculate the amount accumulated every month you save,

until you reach your goal.

Enter the dollar amount to be saved each month: 1

Invalid amount — must save between 5 and 5000 dollars a month. Try again.

Enter the dollar amount to be saved each month: 333.33

Enter the annual interest rate (between 1 and 25): 5.55

Enter the dollar amount of your goal: 5000

Sample Output

Note that dollar amounts are calculated to the nearest penny (i.e. rounded to 2 decimal places),

and the annual interest rate is displayed to 3 decimal places with a % after it.

Month Total

Number Accumulated

—— ———–

1 333.33

2 668.20

3 1004.62

4 1342.60

5 1682.14

6 2023.25

7 2365.94

8 2710.21

9 3056.07

10 3403.54

11 3752.61

12 4103.29

13 4455.60

14 4809.54

15 5165.11