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.
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To find out how much Sophie would have owed after 6 months, we need to calculate the remaining balance on the loan after the initial 3 years.
First, let's calculate the total amount repaid over 3 years:
Total amount repaid = Principal + Interest = $2000 + $900 = $2900
The monthly repayment amount is $40, so the total amount repaid after 3 years is:
Total amount repaid = Monthly repayment amount * Number of months = $40 * 12 * 3 = $1440
Now, let's calculate the remaining balance after 3 years:
Remaining balance = Initial balance - Amount repaid = $2900 - $1440 = $1460
Next, let's calculate the interest on the remaining balance for 6 months, using the same interest rate of 15%:
Interest for 6 months = Remaining balance * (Interest rate / 12) * Number of months = $1460 * (0.15 / 12) * 6 = $109.50
Finally, let's calculate the total amount owed after 6 months:
Total amount owed = Remaining balance + Interest for 6 months = $1460 + $109.50 = $1569.50
Rounding to the nearest dollar, Sophie would have owed $1,570 after 6 months.
To solve this problem, we can start by calculating the total amount Sophie had to repay after 3 years.
The formula to calculate the total amount using simple interest is:
Total amount = Principal + Interest
Given that Sophie borrowed $2000 at an interest rate of 15%, we can calculate the interest as follows:
Interest = Principal * Rate * Time
Interest = $2000 * 0.15 * 3 (since the loan term is 3 years)
Interest = $900
Now, let's find the principal amount:
Principal = Total amount - Interest
Principal = $2000 - $900
Principal = $1100
So, after 3 years, Sophie had to repay a total of $1100 + $900 = $2000.
Now, we need to calculate how much Sophie would owe after 6 months if she repaid $40 per month.
The interest rate remains the same at 15%, so to calculate the interest for 6 months, we use the formula:
Interest = Principal * Rate * Time
Interest = $1100 * 0.15 * (6/12) (since the loan term is now 6 months)
Interest = $82.50
Since Sophie repays $40 per month for 6 months, the total amount she would have repaid is:
Total repayment = $40 * 6
Total repayment = $240
To find the remaining balance, we subtract the total repayment from the total amount:
Remaining balance = Total amount - Total repayment
Remaining balance = $2000 - $240
Remaining balance = $1760
Therefore, after 6 months, Sophie would have owed approximately $1760 (to the nearest dollar) if she repaid $40 per month.