Question 22 (3 marks) Nisa has a credit card on which interest at $17 \%$ per annum, compounded daily, is 3 charged on the amount owing. At the beginning of the month, Nisa owes $\$ 500$ on her credit card. She makes no other purchases using the credit card, but fifteen days later, she repays $\$ 250$. Assuming that interest is charged for the fifteen days, calculate the amount owing on the credit card immediately after the $\$ 250$ payment is made.

Step 1 ：Given that Nisa owes $500 on her credit card at the beginning of the month, the annual interest rate is 17% compounded daily, and she repays $250 after 15 days.

Step 2 ：We first calculate the interest that has been accrued over the 15 days before the payment is made. The formula for compound interest is \(A = P(1 + \frac{r}{n})^{nt}\), 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 (in decimal), \(n\) is the number of times that interest is compounded per year, and \(t\) is the time the money is invested for in years.

Step 3 ：Substituting the given values into the formula, we have \(P = 500\), \(r = 0.17\), \(n = 365\) (since it's compounded daily), and \(t = \frac{15}{365}\) (since it's 15 days).

Step 4 ：Calculating the above expression, we get \(A = 503.5045623306089\).

Step 5 ：Finally, we subtract the $250 payment from the total amount to get the amount owing on the credit card immediately after the payment is made. So, the amount owing is \(503.5045623306089 - 250 = 253.5045623306089\).

Step 6 ：\(\boxed{\text{Final Answer: The amount owing on the credit card immediately after the $250 payment is made is approximately $253.50.}}\)