Sylvia wants to open the Granny Shop. On 6 November 2021, she invests R300 000 into an account earning \( 9,25 \% \) interest per year, compounded monthly. Interest is credited on the first day of every month. Sylvia will move into the Granny Shop on 17 July 2022. If fractional compounding is used for the full period, then the amount that Sylvia has available on 17 July 2022 is A. \( R 319310,96 \) B. \( R 319867,07 \). C. \( R 319860,34 \). D. \( R 319813,24 \).

Step 1: Determine the total number of months from the investment date (6 November 2021) to the withdrawal date (17 July 2022). This is 8 months and 11 days. Step 2: Calculate the monthly interest rate by dividing the annual interest rate by 12. Monthly interest rate = \( \frac{9.25\%}{12} = 0.7708333\% \) or \( 0.007708333 \) in decimal form. Step 3: Use the formula for compound interest to find the amount after 8 months. The formula is: \[ A = P \left(1 + r\right)^n \] where: - \( A \) = the amount of money accumulated after n months, including interest. - \( P \) = principal amount (initial investment). - \( r \) = monthly interest rate (in decimal). - \( n \) = number of months. Step 4: Substitute the values into the formula: \[ A = 300000 \left(1 + 0.007708333\right)^8 \] Step 5: Calculate \( (1 + 0.007708333)^8 \). Step 6: Multiply the result by the principal amount \( 300000 \). Step 7: For the remaining 11 days, calculate the interest for that period using the formula: \[ \text{Interest} = P \times r \times t \] where \( t \) is the fraction of the month (11/30). Step 8: Add the interest from the 11 days to the amount calculated in Step 6 to get the final amount available on 17 July 2022.