Mustafa is saving to buy a house. His goal is $500000. The interest rate is 5% compounded annually, and his plan is to make deposits of $P at the end of every month for 6 years.

a) What is the effective monthly rate?

b) What is $P?

After 2 years, the interest rate changes to 5%.

c) How much money has he saved so far?

d) If he keeps on making the same monthly deposit, how much money will he have saved after 6 years?

e) If he still wants to save exactly $500000 by the end of 6 years, what should his monthly deposit be?

(Don't forget to include the future value of the money from part c)!)