Question

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.

Answer 1

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.