Your $13-$year old cousin comes to you again to ask more questions about the time value of money $($TVM$)$: $$Hey cousin, I want to learn about annuities, growing annuities, perpetuities, and growing perpetuities. Can you please explain what they are? What are their differences? Also, I wonder how all these TVM techniques can be used in real life. How are these techniques applied in finance? Can you provide examples?$$