IME VALUE OF MONEY It is now January 1, 2014; and you will need $1,000 on January 1, 2018, 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, 2018?
b. If you want to make four equal payments on each January 1 from 2015 through 2018 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, 2015 (a year from today), which would you choose? Explain.
d. If you have only $750 on January 1, 2015, what interest rate, compounded annually for 3 years, must you earn to have $1,000 on January 1, 2018?
e. Suppose you can deposit only $200 each January 1 from 2015 through 2018 (4 years). What interest rate, with annual compounding, must you earn to end up with $1,000 on January 1, 2018?
f. Your father offers to give you $400 on January 1, 2015. You will then make six additional equal payments each 6 months from July 2015 through January 2018. If your bank pays 8% compounded semiannually, how large must each payment be for you to end up with $1,000 on January 1, 2018?
g. What is the EAR, or EFF%, earned on the bank account in Part f? What is the APR earned on the account?