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Vanessa bought a house for $268,500
She has a 30 year mortgage with a fixed rate of 6.25%
Vanessa’s monthly payments are $1,595.85
How much was Vanessa’s down payment?
a.
$9,314.45
b.
$16,781.25
c.
$40,275.00
d.
$53,040.00

Respuesta :

W0lf93
The formula for the calculationg of the payment amount during the loan amortization: A = P * (r*( 1+r )^n /(( 1+r )^n - 1 )). Here: A = $1,595.85, n = 12 x 30 = 360, p = 6.25 % so r = 0.0625 : 12 = 0.0052, Therefore: 1,585.95 = P * ( 0.0052 * 1.0052^(360) / 1.0052^(360) ) ; 1585.95 = P * ( 0.0052 * 6.4698 / 5.4698 ) : P = 1,585.95 : 0.0061; P = $259,185.55. Finally the down payment is: 268,500 - 259,185.55 = $9,314.45. Answer: A ) $9,314.45.
Lanuel

Based on the monthly payment calculations, Vanessa’s down payment for her 30 year mortgage would be equal to: A. $9,314.45

Given the following data:

  • Time = 30 years.
  • Cost = $268,500.
  • Interest rate = 6.25% = 0.0625.
  • Monthly payment = $1,595.85.

Note: Interest rate, r = [tex]\frac{0.0625}{12} =0.0052[/tex]

How to calculate monthly payment?

Mathematically, the monthly payment for a mortgage is given by this formula:

[tex]A = \frac{P (r( 1+r )^{nt}}{(( 1+r )^{nt - 1} ))}[/tex]

Substituting the given parameters into the formula, we have;

[tex]1595.85 = \frac{P (0.0052( 1+0.0052 )^{12 \times 30}}{(( 1+0.0052 )^{[12 \times 30] - 1} ))}\\\\1595.85 = \frac{P (0.0052( 1.0052 )^{360}}{(1.0052 )^{359} )}\\\\10271.46=P0.03364\\\\P=\frac{10271.46}{0.03364}[/tex]

P = $259,185.55.

For the down payment, we have:

Down payment =  268,500 - 259,185.55

Down payment = $9,314.45.

Read more on interest rate here: https://brainly.com/question/24341207

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