Answer:
To calculate the interest, final payment, and the amount saved by paying off the loan early, we need to analyze the given information step by step.
1. Interest Calculation:
The formula to calculate simple interest is: Interest = Principal × Rate × Time
Given:
Principal (P) = $6,000.00
Rate (R) = 10% per annum
Time (T) = 24 months
First, we need to convert the time from months to years. Since there are 12 months in a year, T = 24/12 = 2 years.
Using the formula, we can calculate the interest:
Interest = $6,000.00 × 0.10 × 2 = $1,200.00
Therefore, the interest on the loan is $1,200.00.
2. Final Payment Calculation:
After 4 payments, the balance remaining on the loan is $5,082.21. To find the final payment, we need to determine how much of each monthly payment goes towards reducing the principal.
Let's assume X represents the portion of each monthly payment that goes towards reducing the principal. Since the interest is calculated on a simple interest basis, each monthly payment remains constant throughout the loan term.
After 4 payments, the remaining principal can be calculated as follows:
$6,000.00 - (4 × $276.60) = $6,000.00 - $1,106.40 = $4,893.60
Using this information, we can set up an equation:
$4,893.60 + X - ($4,893.60 × 0.10 × (24/12)) = $5,082.21
Simplifying this equation gives us:
X = ($5,082.21 - $4,893.60) + ($4,893.60 × 0.10 × (24/12))
X = $188.61 + $97.87
X = $286.48
Therefore, the final payment is $286.48.
3. Amount Saved by Paying off the Loan Early:
To calculate the amount saved by paying off the loan early, we need to determine the remaining payments if the loan were to continue for the full term of 24 months.
The remaining principal after 4 payments is $4,893.60. We can calculate the remaining balance after 24 months using the formula:
Remaining Balance = Principal + Interest - Total Payments
Total Payments = 4 × $276.60 = $1,106.40
Remaining Balance = $4,893.60 + ($4,893.60 × 0.10 × (24/12)) - $1,106.40
Remaining Balance = $4,893.60 + $978.72 - $1,106.40
Remaining Balance = $4,766.92
The amount saved by paying off the loan early is the difference between the remaining balance after 24 months and the final payment:
Amount Saved = Remaining Balance - Final Payment
Amount Saved = $4,766.92 - $286.48
Amount Saved = $4,480.44
In summary:
- The interest on the loan is $1,200.00.
- The final payment is $286.48.
- By paying off the loan early, Willard Hudson saves $4,480.44.
Explanation: