Question

Suppose you are going to purchase a house. You negotiate a great deal and your bank agrees to lend you money for 30 years at 4% APR (annual percentage rate). The house costs $300,000 and you pay 20% down and finance the rest. Compute (round it to 2 numbers after the decimal point) - do not include $ sign.
(1) Monthly payment: no commas -__________ 2 decimala places.
(2) The interest payment portion of 1st Monthly payment:______ 2 decimal places. 1
(3) The principal payment portion of the 1st Monthly payment:_______ 2 decimal places
(4) Balance after the 1st payment: -no commas and ___________2 decimal places.

Answer 1

Answer:

1. The amount of the house that was financed is;

= 300,000 * ( 1 - 20%)

= $240,000

The amount that will be paid per month is an annuity with the present value being $240,000.

Period = 30 years * 12 months = 360 months

Interest = 4%/12

240,000 = Annuity * (1 - ( 1 + r) ^-n)/r

240,000 = Annuity * ( 1 - ( 1 + 4%/12) ^-n) / r

Annuity = 240,000/209.46

Annuity = $1,145.80

2. Interest Portion;

= Amount Owed * Interest rate

= 240,000 * 4%/12

= $800

3. Principal portion = Monthly payment - Interest

= 1,145.80 - 800

= $345.80

4. Balance after first payment

= Principal - Principal repayment

= 240,000 - 345.80

= $‭239,654.2‬0