Now you have decided that is time to buy a home this is why

Now you have decided that is time to buy a home, this is why you have been trying to build your credit. Research a home that you would love to buy and state the purchase price and a (commonly advertised) interest rate for the mortgage (you may state a rate from a table). Also pick a down payment percent, either 10% i5% or 20%. You will need to open savings account to save for this down payment, find the amount you will need to deposit today into an account at 12% compounded quarterly to build the down payment in 5 years. Using the price of the home and your down payment as well as the finance rate, find the monthly payment of your 30 year mortgage

Solution

Let the total cost of the house be 1,000,000 and down payment requirement be 10% of the cost of the house.

Then the down payment requirement will be 1,000,000 X 10% = 100,000

This down payment amount of 100,000 is required after 5 years so a particular amount will be deposited in saving account today which is yielding 12% interest compounded quaterly.

Calculation of amount to be invested today for down payment:

Let the amount be A.

A X (1+.12*(3/12))^(4*5) = 100,000

On solving the above equation, we get:

A X 1.80611123 = 100,000

A = 55,367.5754

So, today a sum of 55,367.5754 is required to be deposited in a saving account fetching 12% interest compounded quaterly so that after 5 years, the fund value will be 100,000.

Total loan requirement = 1,000,000 - 100,000 = 900,000

Let the monthly payment be M

So, 12M X (1-(1.12^30))/11.4949379 = 9,00,000

On solving the above equation, we get M = 8.918.90

Calculation of 11.4949379:

(1+.12) = (1+(I*(3/12)))^(3/12)

On solving the above equation, we get I = 11.4949379