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

Answer 1

To predict the principal for the first 3 years based on a 4.5% annual decrease, we can calculate the remaining principal at the end of each year.

Starting principal: $320,000

Yearly Calculation:

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

2. Year 2: \[ \text{Principal at Year 2} = \text{Year 1 Principal} \times (1 - 0.045) = 305,600 \times 0.955 = 291,136 \]

3. Year 3: \[ \text{Principal at Year 3} = \text{Year 2 Principal} \times (1 - 0.045) = 291,136 \times 0.955 = 277,664.88 \approx 277,665 \]

Summary Table:

| Year | Principal | |------|---------------| | 0 | $320,000 | | 1 | $305,600 | | 2 | $291,136 | | 3 | $277,665 |

These values reflect the predictions for the principal amount remaining after each year of payments that decrease the principal by 4.5% annually.