First of all, you use the data type int, which cannot hold fractional values (and will implicitly round them towards zero, even before the function is ever called.) You should use double instead, since this is the proper datatype for fractional numbers.

You would also want to use the ceil(x) function, which gives the nearest whole number larger than or equal to x.

#include <math.h>

double calculateCharges(double hours)
{
  if (hours <= 3) {
    return 2.00;
  } else {
    // return $2.00 for the first 3 hours,
    //  plus an additional $0.50 per hour begun after that
    return 2.00 + ceil(hours - 3) * 0.50;
  }
}

To round a float in C, there are 3 <math.h> functions to meet the need. Recommend rintf().

float nearbyintf(float x);

The nearbyint functions round their argument to an integer value in floating-point format, using the current rounding direction and without raising the ‘‘inexact’’ floating point exception. C11dr §7.12.9.3 2

or

float rintf(float x);

The rint functions differ from the nearbyint functions (7.12.9.3) only in that the rint functions may raise the ‘‘inexact’’ floating-point exception if the result differs in value from the argument. C11dr §7.12.9.4 2

or

float roundf(float x);

The round functions round their argument to the nearest integer value in floating-point format, rounding halfway cases away from zero, regardless of the current rounding direction. C11dr §7.12.9.6 2

Example

#include <fenv.h>
#include <math.h>
#include <stdio.h>

void rtest(const char *fname, double (*f)(double x), double x) {
  printf("Clear inexact flag       :%s\n", feclearexcept(FE_INEXACT) ? "Fail" : "Success");
  printf("Set round to nearest mode:%s\n", fesetround(FE_TONEAREST)  ? "Fail" : "Success");

  double y = (*f)(x);
  printf("%s(%f) -->  %f\n", fname,x,y);

  printf("Inexact flag             :%s\n", fetestexcept(FE_INEXACT) ? "Inexact" : "Exact");
  puts("");
}

int main(void) {
  double x = 8.5;
  rtest("nearbyint", nearbyint, x);
  rtest("rint", rint, x);
  rtest("round", round, x);
  return 0;
}

Output

Clear inexact flag       :Success
Set round to nearest mode:Success
nearbyint(8.500000) -->  8.000000
Inexact flag             :Exact

Clear inexact flag       :Success
Set round to nearest mode:Success
rint(8.500000) -->  8.000000
Inexact flag             :Inexact

Clear inexact flag       :Success
Set round to nearest mode:Success
round(8.500000) -->  9.000000
Inexact flag             :Exact

What is weak about OP's code?

(int)(num < 0 ? (num - 0.5) : (num + 0.5))

1. Should num have a value not near the int range, the cast (int) results in undefined behavior.

2. When num +/- 0.5 results in an inexact answer. This is unlikely here as 0.5 is a double causing the addition to occur at a higher precision than float. When num and 0.5 have the same precision, adding 0.5 to a number may result in numerical rounded answer. (This is not the whole number rounding of OP's post.) Example: the number just less than 0.5 should round to 0 per OP's goal, yet num + 0.5 results in an exact answer between 1.0 and the smallest double just less than 1.0. Since the exact answer is not representable, that sum rounds, typically to 1.0 leading to an incorrect answer. A similar situation occurs with large numbers.

OP's dilemma about "The above line always prints the value as 4 even when float num =4.9." is not explainable as stated. Additional code/information is needed. I suspect OP may have used int num = 4.9;.

// avoid all library calls
// Relies on UINTMAX_MAX >= FLT_MAX_CONTINUOUS_INTEGER - 1
float my_roundf(float x) {
  // Test for large values of x 
  // All of the x values are whole numbers and need no rounding
  #define FLT_MAX_CONTINUOUS_INTEGER  (FLT_RADIX/FLT_EPSILON)
  if (x >= FLT_MAX_CONTINUOUS_INTEGER) return x;
  if (x <= -FLT_MAX_CONTINUOUS_INTEGER) return x;

  // Positive numbers
  // Important: _no_ precision lost in the subtraction
  // This is the key improvement over OP's method
  if (x > 0) {
    float floor_x = (float)(uintmax_t) x;
    if (x - floor_x >= 0.5) floor_x += 1.0f;
    return floor_x;
  }

  if (x < 0) return -my_roundf(-x);
  return x; //  x is 0.0, -0.0 or NaN
}

Tested little - will do so later when I have time.

The standard idiom for integer rounding up is:

int a = (59 + (4 - 1)) / 4;

You add the divisor minus one to the dividend.