Nisa has a credit card on which interest at 17% per annum, compounded daily, is charged on the amount owing - HSC - SSCE Mathematics Standard - Question 22 - 2020 - Paper 1

To find the amount owing after 15 days of interest, we use the compound interest formula:

$A = P \left(1 + \frac{r}{n}\right)^{nt}$

Where:

• $A$ is the amount of money accumulated after n years, including interest.
• $P$ is the principal amount (the initial amount of money).
• $r$ is the annual interest rate (decimal).
• $n$ is the number of times that interest is compounded per year.
• $t$ is the time in years.

In this case:

• $P = 500$ (initial debt)
• $r = 0.17$ (17% per annum)
• $n = 365$ (compounded daily)
• $t = \frac{15}{365}$ (15 days as a fraction of a year)

Now substituting these values in:

$A = 500 \left(1 + \frac{0.17}{365}\right)^{365 \times \frac{15}{365}}$

This simplifies to:

$A = 500 \left(1 + \frac{0.17}{365}\right)^{15}$

Calculating this gives:

$A \approx 500 \times 1.0071 \approx 503.55$

So after 15 days, the amount owing is approximately $503.55.

Next, we subtract the repayment made:

$503.55 - 250 = 253.55$

Thus, the amount owing immediately after the payment is made is approximately $253.55.