rbanua61
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HELP PLEASE
The price of a small cabin is $100,000. The bank requires a 5% down payment. The buyer is offered two mortgage options: 20 year fixed at 8% or 30 years fixed at 8%. Calculate the amount of interest paid for each option. How much does the buyer save in interest with the 20 year option?

Respuesta :

Using simple interest, we have that:

  • The amount of interest paid for the 20 year option is $152,000.
  • The amount of interest paid for the 30 year option is $228,000.
  • The buyer saves $76,000 in interest with the 20 year option.

The amount of money accrued in simple interest, after t years, is given by:

[tex]A(t) = Pit[/tex]

In which:

  • P is the initial deposit.
  • i is the interest rate, as a decimal.

In this problem, there is an interest rate of 8%, hence [tex]i = 0.08[/tex].

The down payment is of 5%, hence, the principal is 95% of the price, that is, [tex]P = 0.95(100000) = 95000[/tex]

Then, for the 20 year option, [tex]t = 20[/tex], and:

[tex]A(t) = Pit = 95000(0.08)(20) = 152000[/tex]

The amount of interest paid for the 20 year option is $152,000.

For the 30 year option, [tex]t = 30[/tex], and:

[tex]A(t) = Pit = 95000(0.08)(30) = 228000[/tex]

The amount of interest paid for the 30 year option is $228,000.

228000 - 152000 = 76000

The buyer saves $76,000 in interest with the 20 year option.

A similar problem is given at https://brainly.com/question/13176347