1. **State the problem:** Charlie buys furniture costing 5160 on 25 October with a credit card that has an interest rate of 15.4% per annum compounding daily. The due date for payment is the 22nd of each month, and interest is charged from the purchase date if the balance is not paid by the due date. Charlie pays on 22 December. We need to find the interest charged. 2. **Identify the formula:** The formula for compound interest is: $$ A = P \left(1 + \frac{r}{n}\right)^{nt} $$ where: - $A$ is the amount after interest - $P$ is the principal (5160) - $r$ is the annual interest rate (0.154) - $n$ is the number of compounding periods per year (daily compounding means $n=365$) - $t$ is the time in years 3. **Calculate the time $t$:** - Purchase date: 25 October - Payment date: 22 December - Days from 25 October to 22 November: 28 days (October 25 to November 22) - Days from 22 November to 22 December: 30 days - Total days = 28 + 30 = 58 days - Convert days to years: $t = \frac{58}{365}$ 4. **Calculate the amount $A$:** $$ A = 5160 \left(1 + \frac{0.154}{365}\right)^{365 \times \frac{58}{365}} = 5160 \left(1 + \frac{0.154}{365}\right)^{58} $$ 5. **Calculate the daily interest rate:** $$ \frac{0.154}{365} \approx 0.0004219 $$ 6. **Calculate the compound factor:** $$ \left(1 + 0.0004219\right)^{58} $$ 7. **Calculate the amount $A$ numerically:** $$ A \approx 5160 \times (1.0004219)^{58} $$ Calculate the exponent: $$ (1.0004219)^{58} \approx e^{58 \times \ln(1.0004219)} \approx e^{58 \times 0.0004218} = e^{0.02446} \approx 1.02477 $$ So, $$ A \approx 5160 \times 1.02477 = 5287.58 $$ 8. **Calculate the interest charged:** $$ \text{Interest} = A - P = 5287.58 - 5160 = 127.58 $$ **Final answer:** Charlie is charged approximately 127.58 interest if he pays on 22 December.