\(Mario wants to open a new clothing shop in Pretoria CBD. He estimates that he will have R250 000 available on 16 June 2022 from an investment made on 7 September 2021, earning 7,65\% interest per year, compounded on the first of each month. If fractional compounding is used for the whole period, then the amount Mario deposited on the 7 September 2021 was \)

Step 1: Determine the total number of months from 7 September 2021 to 16 June 2022. This is 9 months and 9 days, which can be approximated as 9.3 months. Step 2: Use the formula for compound interest: A = P(1 + r/n)^(nt), where: - A = the amount of money accumulated after n months (R250,000) - P = the principal amount (the initial deposit) - r = annual interest rate (7.65% or 0.0765) - n = number of times interest is compounded per year (12 for monthly) - t = time in years (9.3/12) Step 3: Rearrange the formula to solve for P: P = A / (1 + r/n)^(nt). Step 4: Substitute the values into the formula: - A = 250,000 - r = 0.0765 - n = 12 - t = 9.3/12 Step 5: Calculate the value of (1 + r/n)^(nt): - r/n = 0.0765/12 = 0.006375 - nt = 12 * (9.3/12) = 9.3 - (1 + 0.006375)^(9.3) ≈ 1.0601 Step 6: Calculate P: P = 250,000 / 1.0601 ≈ 235,000. Step 7: Round to the nearest whole number if necessary.