1. Suppose you plan to retire at age 70, and you want to be able to withdraw an amount of $85,000 per year on each birthday from age 70 to age 100 (a total of 31 withdrawals). If the account which contains your savings earns 6.5% per year simple interest, how much money needs to be in the account by the time you reach your 70th birthday? (Answer to the nearest dollar.)
Hint: This can be solved as a 30-year ordinary annuity plus one withdrawal at age 70, or as a 31-year annuity due.
2. Today is your 25th birthday, and you want to save $1.2 Million by your birthday at age 70. If you expect to earn 6% APR compounded monthly in your retirement account, what constant payment at the end of each month must you deposit into the account through your 70th birthday in order to reach your retirement savings goal on your 70th birthday? (Answer to the nearest penny.)
3. A 7.2% coupon bearing bond pays interest semi-annually and has a maturity of 4 years. If the annual yield to maturity is 5.9%, what is the current price of this bond? (Answer to the nearest penny.)