1. An investment scheme compounds at a rate r at the end of months that end in uary, s in months that end in ber, and t in all other months. You will invest P dollars on January 1st 2020, and hope to have A dollars on January 1st 2021. How much should you invest to day to make this happen?

2. Suppose you lend a friend $100 on January 1st, and in return she offers to pay you back $10 at the start of each month (including this month, for some weird reason) for one year (the last payment is January 1st of the next year). What is the present value of this deal if you assume a market rate of 5% APR compounding monthly? Is the present value worth more than the $100 you leant her?