Question

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) Year Principal 0 $320,000.00 1 $ 2 $ 3 $

Answer 1

To predict the principal for the first 3 years, we will apply a decrease of 4.5% each year.

1. Year 0: The initial principal is $320,000.00.

2. Year 1: We calculate the principal after a 4.5% decrease: \[ \text{Principal after Year 1} = \text{Principal at Year 0} - (\text{Principal at Year 0} \times 0.045) \] \[ = 320,000 - (320,000 \times 0.045) = 320,000 - 14,400 = 305,600.00 \]

3. Year 2: Now we calculate the principal after another 4.5% decrease from the Year 1 principal: \[ \text{Principal after Year 2} = \text{Principal at Year 1} - (\text{Principal at Year 1} \times 0.045) \] \[ = 305,600 - (305,600 \times 0.045) = 305,600 - 13,752 = 291,848.00 \]

4. Year 3: We do the same for the principal after Year 3: \[ \text{Principal after Year 3} = \text{Principal at Year 2} - (\text{Principal at Year 2} \times 0.045) \] \[ = 291,848 - (291,848 \times 0.045) = 291,848 - 13,137.16 = 278,710.84 \]

Now, we can compile the amounts into a table format:

| Year | Principal | |------|-------------------| | 0 | $320,000.00 | | 1 | $305,600.00 | | 2 | $291,848.00 | | 3 | $278,710.84 |

Final values rounded to the nearest hundredth where applicable.