Q. It is now January 1, 2012; and you will need $1,000 on January 1, 2016, in 4 years. Your bank compounds interest at an 8% annual rate?

(a) How much must you deposit today to have a balance of $ 1,000 on January 1, 2016?

(b) If you want to make four equal payments on each January 1 from 2013 through 2016 to accumulate the $1,000, how large must each payment be? (Note that the payments begin a year from today)

(c) If your father offers to make the payments calculated in Part b ($221.92) or to give you $750 on January 1, 2013 (a year from today), which would you choose? Explain.

(d) If you have only $750 on January 1, 2013, what interest rate, compounded annually for 3 years, must you earn to have $1,000 on January 1, 2016?

(e) Suppose you can deposit only $200 each January 1 from 2013 through 2016 (4 years). What interest rate, with annual compounding, must you earn to end up with $1,000 on January 1, 2016?

(f) Your father offers to give you $400 on January 1, 2013. You will then make six additional equal payments each 6 months from July 2013 through January 2016. If your bank pays 8% compounded semiannually, how large must each payment be for you to end up with $1,000 on January 1, 2016?