Problem $2$

You have just won the lottery and you can choose between the following payout options. The annual interest rate

$($EAR$)$ is $10\%.$

a$)$ $$100,000$ right now and $$60,000$ every two years starting $4$ years from now and ending $16$ years from now $($i$.$e$.,$

payments are at t $=0,$ t $=4,$ t $=6,...,$ t $=14,$ t $=16).$

b$)$ $$60,000$ a year for $20$ years with the first payment one year from today $($i$.$e$.,$ payments are at t $=1,2,3...19,$

$20).$

c$)25$ annual payments of $$45,000$ and a $26$th payment of $$299,000.$ The first payment is made right now, and the

$$299,000$ payment is made two years after the last $$45,000$ payment.

How much more is the best option worth today relative to the worst option?