Problem $1$ Assume you are $25$ years old. The IAW insurance company is offering you the following

retirement contract $($called an anmuity$)$: Contribute $$2,000$ per year for the next $40$ years. When

you reach $65$ years of age, you will receive $$30,000$ per year for as long as you live. Assume that

you believe that the chance that you will die is $10\%$ per year after you will have reached $65$ years of

age. In other words, you will reccive the first payment with probability $90\%,$ the second payment

with probability $81\%,$ and so on$.$ Also, assume you will finally die for sure at $105$ years old. If the

prevailing interest rate is $5\%$ per year, all payments occur at year$-$end, and it is now January $1,$

calculate the expected value of this ammity. Is this anmity a good deal? $($Use a spreadsheet.$)$