Problem 1: Time value of money:
It is now January 1, 2006, and you will need $1,000 on January 1, 2010, in 4 years. Your bank compounds interest at an 8 percent annual rate.
a. How much must you deposit today to have a balance of $1,000 on January 1, 2010?
b. If you want to make 4 equal payments on each January 1 from 2007 through 2010 to accumulate the $1,000, how large must each payment be?
(Note that the payments begin a year from today.)
c. If your father were to offer either to make the payments calculated in part b ($221.92) or to give you $750 on January 1, 2007 ( a year from today), which would you choose? Explain.
d. If you have only $750 on January 1, 2007, what interest rate, compounded annually for 3 years, must you earn to have $1,000 on January 1, 2010?
e. Suppose you can deposit only $200 each January 1 from 2007 through 2010 (4 years). What interest rate, with annual compounding, must you earn to end up with $1,000 on January 1, 2010?
f. Your father offers to give you $400 on January 1, 2007. You will then make 6 additional equal payments each 6 months from July 2007 through January 2010. If your bank pays 8 percent, compounded semiannually, how large must each payment be for you to end up with $1,000 on January 1, 2010?
g. What is the EAR, or EFF%, earned on the bank account in part f? What is the APR earned on the account?
Problem 2: Present value of a perpetuity-
What is the present value of a $100 perpetuity if the interest rate is 7 percent? If interest rates doubled to 14 percent, what would its present value be?