Sophie borrowed $2000 at a simple interest rate of 15% for 3 years to repay the loan and has $900 in interest. If Sophie's interest was calculated at the same rate on the balance owing, how much would she have owed after 6 months if she repaid $40 per month? Give your answer to the nearest dollar.

First, we need to find the interest Sophie has to pay every month. To do this, we can use the formula for simple interest:

Interest = Principal × Rate × Time

The total interest that Sophie owes after 3 years is $900.
Principal = $2000
Rate = 15% = 0.15
Time = 3 years = 36 months

So, 900 = 2000 × 0.15 × (36 months) / 12 months
900 = 2000 × 0.15 × (3)
900 = 2000 × 0.45
900 = 900

So, Sophie has to pay a total of $900 in interest. She has to pay this interest over 36 months, or 3 years.

Now, let's find out how much Sophie has to pay every month.
The total amount she has to pay (including interest) is $2000 + $900 = $2900.
Since she has to pay this amount over 36 months, her monthly payment is:
$2900 / 36 months = $80.56 per month

Now, let's find out how much Sophie would have owed after 6 months if she repaid $40 per month.
Sophie has to pay off $80.56 per month for 36 months, so her total payments in the first 6 months would be:
$80.56 * 6 months = $483.36

Now, let's see how much Sophie actually paid in the first six months by only paying $40 per month.
$40 * 6 = $240

Now, let's subtract the amount Sophie actually paid ($240) from the amount she should have paid ($483.36) to find what she still owes after the first six months:
$483.36 - $240 = $243.36

Sophie would still owe $243.36 after the first six months if she repaid $40 per month. Rounded to the nearest dollar, she would owe $243.

To answer this question, we need to calculate Sophie's initial loan amount, given the interest and repayment period. Then, using the simple interest formula, we can calculate the new balance after 6 months.

1. Calculate the initial loan amount:
The interest on the loan is $900, and the interest rate is 15%. We can use the formula:
Interest = Principal × Rate × Time
where Principal is the initial loan amount, Rate is the interest rate, and Time is the loan duration in years.
Substituting the given values:
$900 = Principal × 0.15 × 3
Principal = $900 / (0.15 × 3)
Principal = $900 / 0.45
Principal = $2000

2. Calculate the monthly interest rate:
Since the interest is simple interest and calculated on an annual basis, we need to convert it to a monthly rate.
Monthly Interest Rate = Annual Interest Rate / 12
Monthly Interest Rate = 15% / 12 = 0.0125

3. Calculate the outstanding balance after 6 months:
Since Sophie is making a monthly repayment of $40 for 6 months, we can calculate the total repayment amount:
Total Repayment = Monthly Repayment × Number of Months
Total Repayment = $40 × 6 = $240

Now, we can calculate the remaining loan balance after 6 months by subtracting the total repayment from the principal:
Remaining Balance = Principal - Total Repayment
Remaining Balance = $2000 - $240
Remaining Balance = $1760

4. Calculate the interest accrued on the remaining balance:
The interest is calculated on the remaining balance for 6 months. Using the monthly interest rate, we can calculate the interest:
Interest = Remaining Balance × Monthly Interest Rate × Time
Time = 6 months = 6/12 years
Interest = $1760 × 0.0125 × (6/12)
Interest = $11

5. Calculate the final balance:
Final Balance = Remaining Balance + Interest
Final Balance = $1760 + $11
Final Balance = $1771

Therefore, Sophie would owe approximately $1771 after 6 months if she repaid $40 per month.

To find out how much Sophie would have owed after 6 months, we need to calculate the monthly interest rate and the number of months.

First, let's break down the information given:

Principal amount (borrowed money): $2000
Simple interest rate: 15%
Time period: 3 years
Interest charged: $900

To find the monthly interest rate, we can divide the annual interest rate by 12 (months) and then multiply it by 100 to convert it to a percentage:

15% / 12 = 1.25%

Now, we need to calculate the number of months Sophie has been paying back the loan. Since there are 3 years in total, and she has already paid for 6 months, the remaining time period would be 3 years - 6 months = 2.5 years.

Next, let's calculate the total amount repaid by Sophie during the 6-month period. As she repays $40 per month, the total amount repaid would be $40 * 6 = $240.

Now, let's calculate the interest charged for the 6-month period. Since interest is calculated on the remaining balance, we need to subtract the amount repaid during the 6 months from the original principal amount:

$2000 - $240 = $1760

To calculate the interest charged on this remaining balance, we can use the formula:

Interest = Principal * Rate * Time
Interest = $1760 * (1.25%/100) * (2.5 years)
Interest = $1760 * (0.0125) * (2.5)
Interest = $55

Finally, let's calculate the remaining balance after 6 months:

Remaining balance = Principal + Interest
Remaining balance = $1760 + $55
Remaining balance = $1815

Therefore, Sophie would have owed approximately $1815 after 6 months if she repaid $40 per month.