(a) For this part, use an annual nominal interest rate of 6% compounded monthly. You have signed a one-year lease, to move into your new apartment on 1/1/2021. Your monthly rent is $2,000. On 1/1/2021, you must pay rent for the first month (January) and the last month (December), and then you must pay at the beginning of each month from February to November. (i) What is the present value of all your rent payments as of 1/1/2021? (ii) On 11/1/2020, your landlord, who is in need of money because of the pandemic, proposes that you can pay a lump sum of $23,000 on 11/1/2020 instead of paying rent as described in the lease. If you have enough money to pay your landlord, should you pay the lump sum on 11/1/2020 or pay rent as described in the lease? Base your answer from a present value perspective. (Hint: You should choose the option with lower present value.) (b) Consider the identity +1 = Prove it either algebraically or using time diagrams. If you use time diagrams, you must tell me at which time point(s) you are calculating present values