Step-by-step explanation:
To compare the two options, we can calculate the total amount paid over the life of each loan.
For the 30-year loan:
- Principal (P) = $412,000
- Annual interest rate (r) = 3.85% or 0.0385
- Time (t) = 30 years
Using the formula for calculating the total amount paid on a loan:
Total amount = Principal + Total interest
Total interest = Principal * Annual interest rate * Time
Let's calculate:
Total interest = $412,000 * 0.0385 * 30
Total interest = $473,100
Total amount = $412,000 + $473,100
Total amount = $885,100
For the 15-year loan, we follow the same process:
Total interest = $412,000 * 0.0385 * 15
Total interest = $237,450
Total amount = $412,000 + $237,450
Total amount = $649,450
Comparing the two options, the 15-year loan results in a lower total amount paid ($649,450) compared to the 30-year loan ($885,100). So, the restaurant manager might prefer the 15-year loan if they can afford the higher monthly payments.
