To find the difference in payments between the two loan options for Sandra, we need to calculate the total interest for each loan and then subtract them. Here's how:
Option 1: Vacation loan:
Loan amount: $3000
Interest rate: 4.25% (per year)
Term: 1 year
Interest: Use the compound interest formula (since it's not mentioned if it's simple or compound):
Interest = Principal * Interest rate * Time
Interest = $3000 * 4.25% * 1
Interest ≈ $127.50
Total payment:
Total payment = Principal + Interest
Total payment = $3000 + $127.50
Total payment ≈ $3127.50
Option 2: Simple interest loan:
Loan amount: $3500
Interest rate: 3.25% (simple interest)
Term: 2 years
Interest:
Interest = Principal * Interest rate * Time
Interest = $3500 * 3.25% * 2
Interest = $227.50
Total payment:
Total payment = Principal + Interest
Total payment = $3500 + $227.50
Total payment = $3727.50
Difference in payments:
Now, calculate the difference between the total payments of both options:
Difference = Option 2 payment - Option 1 payment
Difference = $3727.50 - $3127.50
Difference = $600.00
Therefore, Sandra would pay $600.00 more in total if she chooses the simple interest loan with a longer term, even though the loan amount is slightly higher. This is because compounded interest accumulates over time, leading to a higher total cost compared to simple interest with a fixed rate.
Conclusion:
Based on the calculations, Sandra should opt for the vacation loan with a shorter term and lower total interest payments. However, her decision might also depend on other factors like her financial situation and specific loan terms (e.g., early repayment fees).
I hope this explanation helps Sandra make an informed decision!
