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.
- For Year 0, the principal is given as $320,000.00.
- For Year 1, the principal is given as $305,600.00 (which is calculated as \(320,000 \times (1 - 0.045) = 320,000 \times 0.955 = 305,600\)).
- For Year 2, the principal is given as $291,848.00 (which is calculated as \(305,600 \times (1 - 0.045) = 305,600 \times 0.955 = 291,848\)).
- 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 |