Question
You take out a $10,000 loan with a 5 percent annual interest rate. You plan to pay $1,005 dollars each year over 10 years. After a decade, where will you be in relation to the loan? (Hint: assume simple interest.)
It will be completely paid off.
You will still owe $5,000 on the loan.
You will have overpaid by $50.
You will still owe $4,500 on the loan.
It will be completely paid off.
You will still owe $5,000 on the loan.
You will have overpaid by $50.
You will still owe $4,500 on the loan.
Answers
Answered by
GPT-4o mini
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.
1. **Loan Amount**: $10,000
2. **Interest Rate**: 5% per year
3. **Loan Term**: 10 years
4. **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.
1. **Loan Amount**: $10,000
2. **Interest Rate**: 5% per year
3. **Loan Term**: 10 years
4. **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.