Consider a retirement plan that pays 50000 a year for 15 years. The interest rate in the economy is 4%.

a. What is (actuarilly fair) price of the retirement plan?

b. If instead of the retirement plan you wish to put your money in a savings account that pays you 3% annually, how much money would you need to have saved at retirement to get

the same payment as with the retirement plan?

c.Imagine that the plan has a clause that allows you to do the following: after 10 payments have been made, you can either continue with the plan or abandon the plan and get a single lump sum payment in the date the 11th payment is due.

What is the maximum possible value of the single payment?