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Jamie and Eddie are buying an apartment for $320,000. Their loan officer tells them that their principal will decrease by 4.5% every year if they make the minimum mortgage payments. Complete the table to predict the principal for the first 3 years. (Round to the nearest hundredth, if applicable.)(2 points) This table shows the principal amount over the years with missing values to be filled in. Year Principal 0 $320,000.00 1 $ 2 $ 3 $

1 answer

To calculate the principal for each year with a 4.5% decrease, we can follow this formula:

\[ \text{New Principal} = \text{Current Principal} \times (1 - \text{Decrease Rate}) \]

Where the decrease rate is 4.5%, or 0.045 when expressed as a decimal.

Let's fill in the table year by year:

Year 0

  • Principal: $320,000.00

Year 1

Calculate the principal at the end of Year 1: \[ \text{Principal Year 1} = 320,000 \times (1 - 0.045) = 320,000 \times 0.955 = 305,600.00 \]

  • Principal: $305,600.00

Year 2

Calculate the principal at the end of Year 2: \[ \text{Principal Year 2} = 305,600 \times (1 - 0.045) = 305,600 \times 0.955 = 291,856.00 \]

  • Principal: $291,856.00

Year 3

Calculate the principal at the end of Year 3: \[ \text{Principal Year 3} = 291,856 \times (1 - 0.045) = 291,856 \times 0.955 = 278,467.48 \]

  • Principal: $278,467.48 (rounded to $278,467.48)

Completed Table

Now we can fill in the completed table as follows:

| Year | Principal | |------|------------------| | 0 | $320,000.00 | | 1 | $305,600.00 | | 2 | $291,856.00 | | 3 | $278,467.48 |

So, the values to be filled in are:

  • Year 1: $305,600.00
  • Year 2: $291,856.00
  • Year 3: $278,467.48