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 $
2 $
3 $///

Answer 1

To calculate the principal after each year with a decrease of 4.5%, you can use the formula:

\[ \text{New Principal} = \text{Current Principal} \times (1 - \text{decrease rate}) \]

In this case, the decrease rate is 4.5%, which is equivalent to 0.045 in decimal form.

Year 0:

• Principal = $320,000.00

Year 1:

\[ \text{Principal} = 320,000 \times (1 - 0.045) = 320,000 \times 0.955 = 305,600 \]

Year 2:

\[ \text{Principal} = 305,600 \times (1 - 0.045) = 305,600 \times 0.955 = 291,536 \]

Year 3:

\[ \text{Principal} = 291,536 \times (1 - 0.045) = 291,536 \times 0.955 = 278,049.68 \]

Now, rounding to the nearest hundredth where applicable, we can complete the table:

| Year | Principal | |------|------------------| | 0 | $320,000.00 | | 1 | $305,600.00 | | 2 | $291,536.00 | | 3 | $278,049.68 |