Be sure to show all your work.
 

 David and Sam both decided before they went to college that they would like to spend the year after they graduate doing some volunteer humanitarian work in one of the world’s underdeveloped countries before starting their first regular job.  Agreeing with their sons’ noble aspirations, both sets of parents decided to help them work toward that goal by putting $500 in a fund each semester that they were on the Dean’s List.  Both sets of parents used the same bank that paid 8% compounded semiannually.  And both paid into the fund either on Dec. 31 or June 30 after they saw their son’s grades for the semester.
 David studied hard and was on the Dean’s List each semester for his 4 years (8 regular semesters--no summers) of college.  Sam on the other hand worked hard and was on the Dean’s List  each fall semester, but by the spring semester each year, he was so tired of working hard that he goofed off a little and missed being on the Dean’s List by a hair.

 a)  In the fall, when they were each scheduled to depart, how much more did David have in his fund than Sam.

 b)  Develop a formula to find the amount in such a fund paying i% each pay period (semiannually) for n pay periods (let n be an even number) with deposits of $R made only after the fall semester each year.

 c)  Develop a formula to find the amount in such a fund paying i% each pay period (semiannually) for n pay periods (let n be an even number) with deposits of $R made only after the spring semester each year.

 d)  Develop a formula to find the amount in a fund where your Christmas bonus of $R is deposited on Dec. 31 each year but the fund compounds quarterly and pays i% each quarter for n pay  periods (let n be a multiple of 4).
 
 

Filling out the table below may be helpful., but you don't have to use it.  I suggest you practice on David, since you already know what the answer should be.