Final answer:
To find out how much Sacha needs to pay back, we calculate 12 days of compound interest on $1470 at 18.5% per annum, compounding daily, after a 40-day interest-free period. The total amount due includes the original price of the computer and the compounded interest for that 12-day period.
Step-by-step explanation:
The question asks how much Sacha will need to pay back if she buys a computer costing $1470 on her credit card, which imposes an 18.5% per annum interest rate, compounding daily, after a 40-day interest-free period. Sacha plans to pay off the card on March 1st. To calculate the interest, first, determine the number of days interest will be applied to the $1470 amount. Sacha's 30-day statement period plus 10 days interest-free adds up to a 40-day grace period. Since she purchases the computer on day 12, she has 28 days left in the statement period (30 - 12) plus the additional 10 days, totaling 38 days interest-free. From January 10 to March 1 is 50 days. Since interest begins after the grace period, only 12 days of interest (50 days total - 38 days grace period) are applicable. To calculate the compound interest for the 12 days, we use the formula for compound interest: P(1 + r/n)^(nt), where P is the principal amount ($1470), r is the annual interest rate (18.5% or 0.185), n is the number of times the interest is compounded per year (in this case, daily, so 365), and t is the time the money is borrowed for, in years. For 12 days, t would be 12/365. Plugging in the values, we have: Interest = 1470 * (1 + 0.185/365)^(365*(12/365)) - 1470 This calculation will give us the interest amount that Sacha needs to pay in addition to the initial price of the computer.