Answer :
Answer:
$15,283.38 for Loan 2
Step-by-step explanation:
To determine the total amount of money Gracie will pay for each loan option, we can calculate the total repayment amount for each loan.
For Loan 1 with simple interest:
Principal amount (P) = $13,500
Interest rate (r) = 2.7% or 0.027
Time (t) = 5 years
The formula to calculate the total repayment amount for a simple interest loan is:
Total repayment = P + (P * r * t)
Plugging in the values:
Total repayment for Loan 1 = $13,500 + ($13,500 * 0.027 * 5)
Now, calculate:
Total repayment for Loan 1 = $13,500 + ($13,500 * 0.027 * 5) = $13,500 + ($1822.50) = $15,322.50
For Loan 2 with compound interest:
Principal amount (P) = $13,500
Interest rate (r) = 3.2% or 0.032
Time (t) = 4 years
We'll use the compound interest formula to calculate the total repayment amount:
Total repayment = P * (1 + r)^t
Plugging in the values:
Total repayment for Loan 2 = $13,500 * (1 + 0.032)^4
Now, calculate:
Total repayment for Loan 2 = $13,500 * (1 + 0.032)^4 = $13,500 * (1.032)^4 = $13,500 * 1.13217563392
Now, multiply:
Total repayment for Loan 2 ≈ $13,500 * 1.13217563392 ≈ $15,283.38
So, Gracie will pay a total of approximately $15,322.50 for Loan 1 (simple interest) and approximately $15,283.38 for Loan 2 (compound interest). Therefore, Loan 2 with compound interest for 4 years is the cheaper option for Gracie.
