Question:Solve #3. and show your work

Maria and John have been married for 2 years and are trying to start a family.

They have been renting a small apartment and decide they want to purchase a house.

They find one that is selling for $450,000.They have been advised to make a 20% down payment.

1.If they make a 20% down payment on a 20-year mortgage at 3.75%,

a.How much will they need for the down payment?

The down payment is

Downpayment=20%ofSellingprice=0.20450000=$90,000

b.How much will their monthly payment be for the principal and interest?

The amountborrowed is P=45000090000=$360,000.

Data

P=360,000;i=3.75%=0.0375;n=12;r=120.03=0.003125;N=nt=1220=240

Use the present value formula for an ordinary annuity and make A the subject of the formula.

P=A[r1(1+r)N]A[1(1+r)N]=rPA=[1(1+r)N]rP

The monthly payment is

A=[1(1+0.003125)240]0.003125360000=2134.397934$2,134.40

c.How much interest will have been paid if they take the full 20 years to pay off the mortgage?

d. I=NAP=2402134.397934360000=$152,255.50

2.If they use additional savings of $10,000, would it be more advantageous for them to add this amount to the down payment on the house or invest the $10,000 in a bank account that pays 3% interest compounded semi-annually?They would keep the money in the account for the 20 years and not add any additional funds to that account. Explain fully.

If they choose to invest the 10,000 at the 3 % interest rate compounded semi annually instead, they would realized investing would bebetter.

F=P(1+r)N=10000(1+20.03)220=10001.01540=$18,140.18

The interest gained as a result of saving is

Interestgained=18140.1810000=$8,140.18

#3 If they find another mortgage offer of 3.25% for 15 years, would that be a better choice with the 20% down payment?Explain fully.