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)

Answer 1

To calculate the principal for Jamie and Eddie's mortgage over the first three years with a decrease of 4.5% each year, we can follow these steps:

1. Start with the initial amount of the mortgage.
2. Calculate the principal after each year by reducing the previous year's principal by 4.5%.

Here's the calculation in detail:

Year 0 (Initial Principal):

• Initial Principal = $320,000

Year 1:

• Principal after 1 year = Initial Principal × (1 - 0.045)
• Principal after 1 year = $320,000 × (0.955)
• Principal after 1 year = $305,600

Year 2:

• Principal after 2 years = Principal after 1 year × (1 - 0.045)
• Principal after 2 years = $305,600 × (0.955)
• Principal after 2 years = $291,936

Year 3:

• Principal after 3 years = Principal after 2 years × (1 - 0.045)
• Principal after 3 years = $291,936 × (0.955)
• Principal after 3 years = $278,689.68, which rounds to $278,690.00.

Now let's complete the table:

| Year | Principal | |------|-------------------| | 0 | $320,000.00 | | 1 | $305,600.00 | | 2 | $291,936.00 | | 3 | $278,690.00 |

This table shows the projected principal for each of the first three years.