You accept an offer from a Payday Loans company saying that for a fee of $$20,$ you can immediately borrow up to $$400$ for one month. According to this offer, what are $($a$)$ the nominal interest rate per year and $($b$)$ the effective interest rate per year?

How much money will be accumulated in $10$ years from a deposit of $$1,000$ every quarter if the interest rate is $1\%$ per month?