I'm so lost in this class and I need help with this question on my homework, please!?

1.Duke was approved for a 30 year conventional loan for $250,000 at 3.65% fixed rate. He was also approved for a 15 year conventional loan for $250,000 at 3.45% fixed rate. He has $20,000 to put as a down payment. He has to pay insurance of $1400 a year and property tax of $2500 a year. Use time value of money to figure out the best options for Duke. (Be sure to show your work if you are able)

a.To avoid PMI (at least 20% down) what amount would Duke have to put down if he wants to take out the full amount of the loan ($250,000)?

b.If he looks at a house that is $150,000 how much would he pay per month with a 15 year loan?

i.30 year loan?

c.If he looks at a house that is $150,000, would a 30 year loan or a 15 year loan be the best option?

d.He plans to make mortgage payments of no more than $700 a month (this is including escrow). What price of house can he afford?

e.How much more principal will he have to pay per month in order to pay off his house in 7 years if he does the following: $150,000 value home, 25% down payment, 15 year loan.