Please show ALL work for each problem.

27. A perpetuity will pay $900 per year, starting five years after the perpetuity is purchased. What is the present value (PV) of this perpetuity on the date that it is purchased, given that the interest rate is 11%? A) $811 B) $5,390 C) $4,856 D) $8,182 28. You are hoping to have $8,000 in your account 4 years from today in order to go on a trip to hike the Inca Trail in Peru. If your current balance is $6,000, what APR (compounded monthly) would be required if you are to have $8,000 in your account in 4 years? A) B) C) D) 6.01% 7.21% 7.46% 8.3% 29. You would like to give your sister a $9,000 graduation gift when she graduates from college. You have $8,000 in your savings account and the bank pays an interest rate of 4% APR compounded semi-annually. How long will it take before you have enough money for the $9000 gift? A) Less than 2 years B) Between 2 and 3 years C) Between 3 and 4 years D) Between 5 and 6 years