$1.$ Two years ago, Paul borrowed $$10000$ from his sister Gerri to start a business. Paul agreed

to pay Gerri interest for the loan at the rate of $4\%/$year$,$ compounded monthly. Paul will

now begin repaying the amount he owes by amortizing the loan $($plus the interest that has

accrued over the past $2$ years$)$ through monthly payments over the next $5$ years at an interest

rate of $3\%/$year compounded monthly.

a$)$ Find the size of the monthly payments Paul will be required to make.

b$)$ Find the outstanding principal at the end of $3$ years.$($Using formula$)$