The 'time value of money' is $($along with 'risk and return' and the importance of options$)$ one of the core concepts in finance. This concept is important not just in corporate finance or investment settings, but also in personal finance $($i$.$e$.,$ your everyday life$).$ Based on what you have learned in class $($from the textbook, lectures, practice problems, etc$)$ and your own personal experiences, answer the following questions. Wherever possible, use examples to illustrate your responses.

Looking back, can you think of situations where you or someone you have advised $($e$.$g$.,$ a parent, sibling, child$)$ may have made a different decision if you had used time value calculations to analyze your options?

Consider a mortgage with a balance of $$250,000,$ that carries a $5\%$ fixed$-$rate interest and has $30$ years remaining to maturity. Would you benefit in any way from making an extra payment of $$100$ each month on the mortgage? If so$,$ is there any reason not to make the extra payment? Explain.

Present and future value calculations are dependent upon the interest rates used in the calculations. What does the interest rate represent, conceptually? In a later section of the course we will discuss in great detail how to identify and measure appropriate discount rates, so I am NOT looking for a statistically or numerically$-$focused discussion here. Something more along the lines of what does it mean, economically, to say that the discount rate is $10\%$ instead of $5\%?$