Use the annuity formula to calculate the monthly mortgage payment for a 30 year, $500,000 home loan with a fixed annual rate of 5%. How much of your first payment is principle? Please show all work and formulas.

Then, the first tranche of a just issued $100 million (total principle value) CMO has a principle of $1million. The underlying mortgages in the pool all have an interest rate of 5% and the average mortgage has a principle of $500,000. Using the principle amount you just calculated, and assuming the value won't change substantially for the first couple of payments, how long will it be before this first tranche is retired assuming there are no pre-payment? Please show all work.