Calculate the Savings Rate You Actually Need

"Save more" is useless advice when you need a number. Give it your goal, target amount, current savings, income and expected return, and it walks the maths step by step to the monthly and percentage savings rate that gets you there by the deadline. Suits anyone who wants the actual figure rather than a vague nudge to tighten up.

I want to understand exactly what savings rate I need to hit my financial goal on time. Please walk me through the maths step by step.

My situation:
- Financial goal: {GOAL_DESCRIPTION}
- Target amount: {TARGET_AMOUNT}
- Current savings toward this goal: {CURRENT_SAVINGS}
- Gross annual income: {ANNUAL_INCOME}
- Net monthly income: {NET_MONTHLY_INCOME}
- Expected annual return on savings: {EXPECTED_RETURN}%
- Target date: {TARGET_DATE}

Please: (1) calculate the required monthly saving amount, (2) express this as a percentage of my net income (my required savings rate), (3) show the compound interest effect if I invest rather than hold cash, (4) explain what happens if I start 6 or 12 months late, and (5) define what a 'good' savings rate looks like for my goal type. Show all calculations clearly.