Final answer:
Sacha will owe the original purchase price of the computer, $1470, since she pays back the amount before any interest is compounded on her purchase. The question's options do not accurately reflect the correct amount due, as the actual payback amount does not reach even the lowest provided option of $1500.
Step-by-step explanation:
To calculate the amount Sacha will need to pay back for her computer purchase on her credit card, we need to consider the interest rate, the length of the interest-free period, and the time at which the first interest will be charged.
Sacha's bank offers a 30-day statement period and an additional 10 days interest-free. Since she makes the purchase on day 12 of the statement period, she has 18 days remaining in this period plus 10 more days, totaling 28 days interest-free. If she pays on 1 March, then she will only be charged interest for the days in February (since January has 31 days).
February typically has 28 days, but on a leap year, it has 29 days. Since the interest compounds daily, we need to calculate the daily interest rate which is the annual rate divided by the number of days in a year. In this case, 18.5% per annum would be:
18.5% / 365 = 0.05068% per day (or 0.0005068 as a decimal).
If we use a non-leap year with 28 days in February, Sacha would be charged for 28 - 28 = 0 days of interest. In a leap year with 29 days in February, she would owe for 1 day of interest:
Interest for 1 day = $1470 * 0.0005068 = $0.744996, which would not increase the balance enough to reach even the first option of $1500. Therefore, Sacha would need to pay $1470, which is not listed in any of the provided options.
Since Sacha pays before any interest accumulates, she will owe only the original amount of $1470.