$1)$ What is the relationship between discounting and compounding?$2)$ Compute the following:a$)$ You invest $$16,000$ today at $9$ percent per year. How much will you have after $15$ years?b$)$ What is the current value of $$130,000$ after $10$ years if the discount rate is $12$ percent?c$)$ You invest $$3,500$ a year $($at the end of a period$)$ for $20$ years at $11$ percent. How much will you have after$20$ years?$3)$ How much should you set aside each year $($end of the period$)$ to accumulate $$80,000$ after $15$ years? The interest rate is $10$ percent.$*$Use the PV$-$FV tables to solve all problems and show how you arrived at your answer.