Answer:
- Financing Amount: $4,840
- Interest Rate on 2-Year Loan: 4.5%
- Interest Rate on 5-Year Loan: 6%
Explanation:
- Financing Amount: $4,840
- Interest Rate on 2-Year Loan: 4.5%
- Interest Rate on 5-Year Loan: 6%
To explain the answer, let's calculate the monthly and total cost for each loan term using the given information:
2-Year Loan:
To calculate the monthly cost, we need to use the formula for calculating the monthly payment on a loan. The formula is as follows:
Monthly Payment = [P * r * (1 + r)^n] / [(1 + r)^n - 1]
Where:
P = Loan amount
r = Monthly interest rate (annual interest rate / 12)
n = Number of monthly payments
Using the given information for the 2-year loan:
P = $4,840
r = 4.5% / 12 = 0.375%
n = 2 years * 12 months/year = 24 months
Plugging in the values into the formula, we get:
Monthly Payment = [$4,840 * 0.00375 * (1 + 0.00375)^24] / [(1 + 0.00375)^24 - 1]
Using a calculator, the monthly payment comes out to around $208.50.
To calculate the total cost, we need to multiply the monthly payment by the number of monthly payments:
Total Cost = Monthly Payment * Number of Months
Total Cost = $208.50 * 24 = $5,004
Therefore, the monthly cost on a 2-year loan with a 4.5% interest rate is approximately $208.50, and the total cost over the 2-year period would be around $5,004.
5-Year Loan:
Similar to the 2-year loan, we can calculate the monthly and total cost for the 5-year loan using the same formula.
Using the given information for the 5-year loan:
P = $4,840
r = 6% / 12 = 0.5%
n = 5 years * 12 months/year = 60 months
Plugging in the values into the formula, we get:
Monthly Payment = [$4,840 * 0.005 * (1 + 0.005)^60] / [(1 + 0.005)^60 - 1]
Using a calculator, the monthly payment comes out to around $93.48.
To calculate the total cost, we need to multiply the monthly payment by the number of monthly payments:
Total Cost = Monthly Payment * Number of Months
Total Cost = $93.48 * 60 = $5,608.80
Therefore, the monthly cost on a 5-year loan with a 6% interest rate is approximately $93.48, and the total cost over the 5-year period would be around $5,608.80.
