public static void main(String[] args) {
    Timer timer = new Timer();
    timer.scheduleAtFixedRate(new TimerTask() {
        
        @Override
        public void run() {
            System.out.println(new Date(this.scheduledExecutionTime()));
        }
        
    }, 500L, 1000L);
}

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Mon Jul 02 14:34:20 CST 2018
Mon Jul 02 14:34:21 CST 2018
Mon Jul 02 14:34:22 CST 2018
Mon Jul 02 14:34:23 CST 2018
Mon Jul 02 14:34:24 CST 2018
Mon Jul 02 14:34:25 CST 2018

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/**
 * The state of this task, chosen from the constants below.
 */
int state = VIRGIN;

/**
 * This task has not yet been scheduled.
 */
static final int VIRGIN = 0;

/**
 * This task is scheduled for execution.  If it is a non-repeating task,
 * it has not yet been executed.
 */
static final int SCHEDULED   = 1;

/**
 * This non-repeating task has already executed (or is currently
 * executing) and has not been cancelled.
 */
static final int EXECUTED    = 2;

/**
 * This task has been cancelled (with a call to TimerTask.cancel).
 */
static final int CANCELLED   = 3;

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public void schedule(TimerTask task, long delay, long period) {
    if (delay < 0)
        throw new IllegalArgumentException("Negative delay.");
    if (period <= 0)
        throw new IllegalArgumentException("Non-positive period.");
    sched(task, System.currentTimeMillis()+delay, -period);
}

public void scheduleAtFixedRate(TimerTask task, long delay, long period) {
    if (delay < 0)
        throw new IllegalArgumentException("Negative delay.");
    if (period <= 0)
        throw new IllegalArgumentException("Non-positive period.");
    sched(task, System.currentTimeMillis()+delay, period);
}

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If an execution is delayed for any reason (such as garbage collection or other background activity), subsequent executions will be delayed as well. In the long run, the frequency of execution will generally be slightly lower than the reciprocal of the specified period (assuming the system clock underlying Object.wait(long) is accurate). As a consequence of the above, if the scheduled first time is in the past, it is scheduled for immediate execution. 

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If an execution is delayed for any reason (such as garbage collection or other background activity), two or more executions will occur in rapid succession to "catch up." In the long run, the frequency of execution will be exactly the reciprocal of the specified period (assuming the system clock underlying Object.wait(long) is accurate). 

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private void sched(TimerTask task, long time, long period) {
    if (time < 0)
        throw new IllegalArgumentException("Illegal execution time.");

    // Constrain value of period sufficiently to prevent numeric
    // overflow while still being effectively infinitely large.
    if (Math.abs(period) > (Long.MAX_VALUE >> 1))
        period >>= 1;

    synchronized(queue) {
        if (!thread.newTasksMayBeScheduled)
            throw new IllegalStateException("Timer already cancelled.");

        synchronized(task.lock) {
            if (task.state != TimerTask.VIRGIN)
                throw new IllegalStateException(
                    "Task already scheduled or cancelled");
            task.nextExecutionTime = time;
            task.period = period;
            task.state = TimerTask.SCHEDULED;
        }

        queue.add(task);
        if (queue.getMin() == task)
            queue.notify();
    }
}

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/**
 * The main timer loop.  (See class comment.)
 */
private void mainLoop() {
    while (true) {
        try {
            TimerTask task;
            boolean taskFired;
            synchronized(queue) {
                // Wait for queue to become non-empty
                while (queue.isEmpty() && newTasksMayBeScheduled)
                    queue.wait();
                if (queue.isEmpty())
                    break; // Queue is empty and will forever remain; die

                // Queue nonempty; look at first evt and do the right thing
                long currentTime, executionTime;
                task = queue.getMin();
                synchronized(task.lock) {
                    if (task.state == TimerTask.CANCELLED) {
                        queue.removeMin();
                        continue;  // No action required, poll queue again
                    }
                    currentTime = System.currentTimeMillis();
                    executionTime = task.nextExecutionTime;
                    if (taskFired = (executionTime<=currentTime)) {
                        if (task.period == 0) { // Non-repeating, remove
                            queue.removeMin();
                            task.state = TimerTask.EXECUTED;
                        } else { // Repeating task, reschedule
                            queue.rescheduleMin(
                              task.period<0 ? currentTime   - task.period
                                            : executionTime + task.period);
                        }
                    }
                }
                if (!taskFired) // Task hasn't yet fired; wait
                    queue.wait(executionTime - currentTime);
            }
            if (taskFired)  // Task fired; run it, holding no locks
                task.run();
        } catch(InterruptedException e) {
        }
    }
}

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currentTime = System.currentTimeMillis();
executionTime = task.nextExecutionTime;
if (taskFired = (executionTime<=currentTime)) {
    if (task.period == 0) { // Non-repeating, remove
        queue.removeMin();
        task.state = TimerTask.EXECUTED;
    } else { // Repeating task, reschedule
        queue.rescheduleMin(
          task.period<0 ? currentTime   - task.period
                        : executionTime + task.period);
    }
}

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