To analyze the situation, we need to calculate the total interest on the loan and the total amount you will pay over the 10 years.
- Loan Amount: $10,000
- Interest Rate: 5% per year
- Loan Term: 10 years
- Annual Payment: $1,005
Calculate Total Interest
Using simple interest, the total interest \( I \) can be calculated using the formula:
\[ I = P \times r \times t \]
Where:
- \( P \) is the principal (loan amount)
- \( r \) is the rate of interest (as a decimal)
- \( t \) is the time in years
Substituting the values:
\[ I = 10,000 \times 0.05 \times 10 = 10,000 \times 0.5 = 5,000 \]
Total Repayment Amount
The total amount you will need to repay after 10 years is:
\[ \text{Total Repayment} = \text{Principal} + \text{Total Interest} = 10,000 + 5,000 = 15,000 \]
Total Payments Made
Over 10 years, you will make payments of $1,005 each year. The total payments made will be:
\[ \text{Total Payments} = 1,005 \times 10 = 10,050 \]
Compare Total Payments to Total Repayment Amount
Now, let's compare:
- Total Amount to be Repaid: $15,000
- Total Payments Made: $10,050
Remaining Balance
At the end of 10 years, the remaining balance will be:
\[ \text{Remaining Balance} = \text{Total Repayment} - \text{Total Payments Made} = 15,000 - 10,050 = 4,950 \]
Conclusion
After 10 years, you will still owe $4,950 on the loan. Among the given options, none includes this value exactly, but it's closest to "You will still owe $4,500 on the loan."
So, the most accurate response based on the calculations provided is that none of the provided options is completely correct, but the situation is that you will owe approximately $4,950 after 10 years, indicating that you will still owe more than $4,500.