You expect to receive $$2,000$ every year for the next $8$ years, beginning at the end of the first year, except for year $4$ when you will receive nothing.

a$)$ What is the future value of these receivables in year $10$ if the interest rate is $6\%?$

b$)$ You approach a bank for a $15-$year mortgage of $$350,000.$ The bank approves the request at a rate of $6\%$ payable monthly. What is your monthly payment? What is the interest and principal paid at the end of the $5$th year $(60$th month$)?$

c$)$ Explain briefly the concept of interest rate compounding to Grandma.