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)

Question

Year Principal
0 $320,000.00
1 $305,600.00
2 $291,848.00
3 $

Answer 1

To find the principal for the third year, we'll continue applying the 4.5% decrease based on the previous year's principal.

The formula for calculating the principal after the decrease is:

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

The decrease rate is 4.5%, or 0.045 in decimal form.

1. For Year 0, the principal is given as $320,000.00.
2. For Year 1, the principal is given as $305,600.00 (which is calculated as \(320,000 \times (1 - 0.045) = 320,000 \times 0.955 = 305,600\)).
3. For Year 2, the principal is given as $291,848.00 (which is calculated as \(305,600 \times (1 - 0.045) = 305,600 \times 0.955 = 291,848\)).
4. Now, for Year 3, we will calculate it using Year 2's principal.

Calculating for Year 3:

\[ \text{Principal for Year 3} = 291,848 \times (1 - 0.045) = 291,848 \times 0.955 \]

Calculating the value:

\[ 291,848 \times 0.955 \approx 278,922.64 \]

Thus, rounding to the nearest hundredth, the principal for Year 3 will be:

\[ \text{Principal} \approx $278,922.64 \]

So, the completed table is as follows:

| Year | Principal | |------|------------------| | 0 | $320,000.00 | | 1 | $305,600.00 | | 2 | $291,848.00 | | 3 | $278,922.64 |