For a 30 -year monthly level-pay home mortgage loan of \(\$ 500,000\) with a \(3 \%\) interest rate

(a) Compute the monthly level payment.

(b) What is the total amount of interest you pay during the loan?

(c) After how many periods have you paid off half of the principal? Find \(n\) where \(B_{n-1}>\$ 250,000, B_{n} \leq \$ 250,000\).

(d) After how many periods does the monthly payment start to cover more of the principal than the interest: Find \(n\) where \(I_{n-1}>L / 2\), \(I_{n} \leq L / 2\).