Problem $1.$

A major lottery advertises that it pays the winner $$10$ million. However this prize money is paid at the

rate of $$500,000$ each year $($with the first payment being immediate$)$ for a total of $20$ payments. What is the

present value of this prize at $10\%$ interest compounded annually?

Report your answer in $ millions, rounded to two decimal places.

Problem $2.$

A young couple has made a deposit of the first month's rent $($equal to $$1,000)$ on a $6-$month apartment lease. The deposit is refundable at the end of six months if they stay until the end of the lease.

The next day they find a different apartment that they like just as well, but its monthly rent is only $$900.$ And they would again have to put a deposit of $$900$ refundable at the end of $6$ months.

They plan to be in the apartment only $6$ months. Should they switch to the new apartment? Assume an $($admittedly unrealistic!$)$ interest rate of $12\%$ per month compounded monthly. Please choose your answer

and explain.

$-$Stay

$-$Switch