Finance computations

Solution is available here for U$1.50

Question 1:
Ricky and Lucy have decided to refinance their home mortgage loan. Their current home mortgage loan is for $600,000. The mortgage interest rate is 5.75% and it is to be paid off in 30 years with equal monthly payments. After 3 full years of payments, Ricky and Lucy will refinance the balance at 3.0%, to be paid off in 15 years with equal monthly payments. What will Ricky and Lucy's new monthly payments be?

Question 2:
One of the largest automobile dealers in the city advertises a 4-year old car for sale as follows:
• Cash price $6599
Or
• A down-payment of $1000 with 48 monthly payments of $179.99
Questions: A student bought the car and made a down payment of $2000. The dealer charged her the same interest rate used in the advertised offer.
a) How much will the student pay each month for 48 months? Show calculations.
b) What effective annual interest rate is being charged? Show calculations and formula. Please show me the all steps that lead to the answers.

Question 3:

You want to bank enough money to pay for 5 years of undergraduate school plus 3 years of graduate school, at $37,000 per year for your child. The savings account will pay an interest rate of 3.0% per year. The first annual payment for tuition and for room and board will be made in 10 years. If you deposit the money today, how much must you deposit? Show calculations.