Computing Compound Interest

A simple savings account earns compound interest over time, based upon an annual interest rate (e.g., 1% or 9%) per year. The basic computations proceed as follows:

A monthly interest rate is computed:

monthly_rate = annual_rate_percent / 1200.0;

The monthly rate determines the interest the bank adds to the account each month, according to the formula:
```
interest = monthly_rate * (old balance)
new balance = (old balance) + interest
```

For example, at an annual rate of 8%, the monthly rate is 0.00666667. With a starting balance of $100, the computations proceed as follows for the first year:

       Starting   Monthly   Ending
Month   Balance   Interest  Balance
  0      ------     ----     100.00
  1      100.00     0.67     100.67
  2      100.67     0.67     101.34
  3      101.34     0.68     102.01
  4      102.01     0.68     102.69
  5      102.69     0.68     103.38
  6      103.38     0.69     104.07
  7      104.07     0.69     104.76
  8      104.76     0.70     105.46
  9      105.46     0.70     106.16
 10      106.16     0.71     106.87
 11      106.87     0.71     107.58
 12      107.58     0.72     108.30

This problem asks to you

write a procedure compute_until_double that computes monthly balance until the amount in the account doubles from the initial balance.
write a program that uses compute_until_double in several ways.

The following notes provide additional information regarding this work.

procedure compute_until_double
- The procedure should have the following signature:
```
void compute_until_double(double initial_balance, double annual_rate,
                         char print_option, int *months_to_double)
```
  - initial_balance gives the initial balance, before any interest has accrued.
  - annual_rate gives the annual percentage interest rate
  - print_option specifies one of three alternatives:
    - 'n': no printing is to be done by the procedure
    - 'm': the status of the account (i.e., month number, starting balance, interest for that month, and ending balance) is printed every month.
    - 'y': the status of the account (i.e., year number, starting balance, interest for that year, and ending balance) is printed every year (i.e., every 12 months).
- months_to_double refers to an integer variable in the main program, and the number of months required for the account balance to double is stored in this variable when the procedure concludes.
- Processing in compute_until_double continues until the balance in the account doubles from its original value.
- Regardless of what printing option is selected, compute_until_double may have only one loop. Within the loop, the print_option should be consulted to determine whether or not to print the account balance for that loop iteration.
The program should compute and print the following:
- An initial table should be printed, giving a monthly status report for an account that starts with $100 at an 8% annual percentage rate. (That is, the first part of this table should agree exactly with the sample table given above — although spaces on a line may be inserted or deleted.)
- A second table should be printed, giving an annual status report for an account that starts with $300 at a 2% annual percentage rate.
- Starting with $100.00 in an account, the program should print a table giving the number of months for the account to double with annual interest rates of 1%, 2%, 3%, ..., 9%.

Grading

In addition to the general grading guidelines for evaluation, the assignment is worth 25 points.

[15 points] Procedure computeUntilDouble

[6 points] Correctness of computations in the main loop
[2 points] Correct printing for the 'n' option
[2 points] Correct printing for the 'm' option
[2 points] Correct printing for the 'y' option
[3 points] Correct storage of the months to double in the location referenced by months_to_double

[6 points] Main program

[2 points] Computation and printing of monthly table
[2 points] Computation and printing of annual table
[2 points] Computation and printing of months to double

Comments on Program Format, Comments, Readability, etc.
(Points not given, but points can be deducted.)
[4 points] Testing
- Test Plan with a numbered listing of the circumstances that can reasonably arise in this problem
- Listing of test cases to be considered, with the expected outcome
- Listing of actual test runs
- Statement of why the program is correct