Question

Nicole took out a 30-year mortgage for $90,000 at 7.5%. How much is her monthly mortgage payment? I assume $675,000?

Answer 1

Answer:

• Nicole pays $629.29 per month
• Zack pays $563.24 per month

Step-by-step explanation:

We're not quite sure why you estimated the monthly payment at several times the value of the entire loan.

The applicable formula is the amortization formula. It computes the monthly payment A on loan principal value P at annual rate r for t years to be ...

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

The value of r used in this formula is the decimal equivalent of the percentage rate. 7.5% = 0.075; 9% = 0.09

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a)

The formula with Nicole's numbers filled in looks like ...

  A = $90,000(0.075/12)/(1 -(1 +0.075/12)^(-12·30))

  = $90,000(0.00625)/(1 -(1.00625^-360)) = $562.50/(1 -0.1051398)

  A ≈ $629.293 ≈ $629.29 . . . . Nicole's monthly payment

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b)

Using the same formula with P=$70,000, r=0.09, t=30, we find Zack's monthly payment to be $563.24.

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Additional comment

If you're doing a number of problems of this type, it can be helpful to use a tool that will do the calculation for you without error. A graphing calculator or spreadsheet can do that. One example is shown in the attachment.