Algebra question help please

Question

Raymond and Kevin want to purchase a house. They offer $807,000 with 20% down payment. They are pre-qualified for a 30-year loan at 3.1%. Calculate their anticipated monthly payments.

Answer 1

Greetings Anthony,

Assuming the interest rate is fixed we are going to use this formula m = (P*r(1+r)ⁿ) / ((1+r)ⁿ-1)

Defining our variables:

m: Monthly payment

P: Principal amount (the amount taken out as a loan)

r: Interest rate per month

n: Total amount of payments due

To find P, we use the information regarding their down payment. With $807,000 being 20% of the down payment we can multiply $807,000 * 5 to find out the total price of their expensive home. We then minus $807,000 from this number to find the amount they take out as a loan which is $3,228,000. Hopefully one day I'll be able to afford a home like Raymond and Kevin B)

P = $3,228,000

To find r, we convert 3.15% to a decimal, .0315. We then divide this by 12 to find the interest due per month.

r = .0315 / 12

to find n, we multiply the total amount of years by months per year. 30 * 12 = 360

n = 360

Plugging this information into our formula results in the monthly payments.

(32288000*(.0315/12)*(1+(.0315/12)³⁶⁰)) / ((1+(.0315/12))³⁶⁰-1) = 13871.90657607

We then round this number to the nearest cent resulting in:

$13871.91 as their anticipated monthly payment.

Hope this helps :)