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Aya and Sakura have now saved up their down payment to buy a home, but they still need to borrow to cover the rest. For the home they want this will require a mortgage of $450,000 to cover the remaining amount and they’re not sure whether they could afford the monthly loan payments. The bank has offered them a mortgage interest rate of 3.25%, compounded monthly .

How much would they have to be able to afford to pay each month in order to pay off their mortgage in 25 years?

What is the total amount that would be paid to the lender after 25 years of payments?

Respuesta :

Using compound interest, it is found that:

  • The total amount that would be paid is of $1,012,978.
  • The would have to afford to pay $3,376.6 each month.

What is compound interest?

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

  • A(t) is the amount of money after t years.
  • P is the principal(the initial sum of money).
  • r is the interest rate(as a decimal value).
  • n is the number of times that interest is compounded per year.
  • t is the time in years for which the money is invested or borrowed.

In this problem:

  • The mortgage is of $450,000, hence [tex]P = 450000[/tex].
  • Over a period of 25 years, hence [tex]t = 25[/tex].
  • The interest rate is of 3.25%, hence [tex]r = 0.0325[/tex].
  • The amount is compounded monthly, hence [tex]n = 12[/tex].

Then, the amount paid in 25 years is given by:

[tex]A(25) = 450000\left(1 + \frac{0.0325}{12}\right)^{12(25)} = 1012978[/tex]

The total amount that would be paid is of $1,012,978.

Considering 25 years of 12 months, the monthly amount paid is given by:

[tex]M = \frac{1012978}{25(12)} = 3376.6[/tex]

The would have to afford to pay $3,376.6 each month.

To learn more about compound interest, you can take a look at https://brainly.com/question/25781328

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