Alexandra bought a $315,000.00 house, paying 10% down, and financing the rest at 6% interest for 20
years.
A. What is the monthly payment?
Alexandra has a payment of
a month.
B. How much interest will be paid over the life of the loan?
Alexandra will pay
in interest over the life of the loan.

Respuesta :

Answer:

  A. payment: $2031.08

  B. interest: $203,959.20

Step-by-step explanation:

There are many financial calculators, apps, and spreadsheets that will solve this for you. Here, we will use the amortization formula that would be implemented by one of those.

A.

The monthly payment is given by ...

  A = P(r/12)/(1 -(1 +r/12)^(-12t)) . . . loan of P at rate r for t years

If 10% is put down on the house, then amount that needs to be financed will be ...

  $315,000 × (1 -10%) = 0.90 × $315,000 = $283,500

For interest rate 6% and a period of 20 years, the monthly payment is ...

  A = $283,500(0.06/12)/(1 -(1 +0.06/12)^(-12·20))

  A = $283,500(0.005)(1 -(1.005^-240)) ≈ $2,031.08

__

B.

The interest is the difference between the amount repaid and the original loan value:

  interest = 240 × $2031.08 - 283,500 = $487,459.20 -283,500

  interest = $203,959.20