Final answer:
The question asks to calculate the present value of a retirement annuity where payments and interest rates are given. It involves annuity computations and the use of the future value formula adjusted for semi-annual compounding to find the initial investment needed.
Step-by-step explanation:
The question involves calculating the present value of a retirement annuity. Ms. G Du Randt will receive R108,000 every 6 months for 32 years at a semi-annual interest rate of 9.5%. This scenario illustrates a future value annuity calculation based on a fixed interest rate and a certain number of payments. By using the given annuity formula FV = P × [(1 + r/n)^(nt) - 1] × (1 + r/n), we can isolate the variable P (the present value) and solve for the initial investment needed (P) that would yield this annuity. The formula takes into account the semi-annual compounding by dividing the annual rate by 2 to find the rate per half-year and squaring the number of years to get the total number of periods.
However, in order to calculate the present value accurately, one would need correct financial formulae and probably a financial calculator or specialized software as manual calculations are complex and prone to error. Financial mathematics can be quite challenging, but it provides valuable information for personal financial planning, especially for retirement planning.