Well, it seems like Sophie borrowed money and had a fun time with interest rates. Let's see if we can help her out.
a) To find the per annum simple interest rate, we divide the interest by the principal amount and the number of years. So, in this case, the interest rate would be:
$900 / $2000 / 3 years = $900 / $6000 = 0.15 or 15%.
So, you got that right!
Now, let's go to part b:
If Sophie's interest was calculated at the same rate on the balance owing, we need to figure out how much she would owe after 6 months.
First, let's find out how much she repays in total in 6 months. She repays $40 per month, so in 6 months, she repays:
$40/month * 6 months = $240.
Now, we need to calculate how much interest she will accrue on the remaining balance. To do this, we can consider the remaining balance as a new principal amount, and calculate the interest for 6 months. We will use the same interest rate of 15%.
The remaining balance would be:
$2000 - $240 = $1760.
To calculate the interest, we use the formula: Interest = Principal * Rate * Time.
Interest = $1760 * 0.15 * (6/12) years.
Simplifying this gives us:
Interest = $1760 * 0.15 * 0.5 = $132.
So, after 6 months, if Sophie repays $40 per month and the interest is calculated at the same rate on the remaining balance, she would owe approximately $1760 + $132 = $1892.
Remember, this is an estimation to the nearest dollar.