Final answer:
The value of the investment at the end of 6 years is calculated by determining the compound interest earned on the initial deposit and additional deposits made at different times during the period.
Step-by-step explanation:
(a) The timeline for the investment is as follows:
T0: Initial deposit of R150,000
T1: Deposit of R8,000
T5: Deposit of R2,000
T6: End of the 6-year period
(b) To calculate the value of the initial deposit made at T0 at the end of T6, we need to calculate the compound interest earned over the 6-year period. For the first 4 years, the interest rate is 12% p.a. compounded half-yearly, and for the remaining 2 years, the interest rate is 8.5% p.a. compounded yearly. Using the compound interest formula, we can calculate the value of the initial deposit at T6 to be R191,289.27.
(c) To calculate the value of the deposit made at T1 at the end of T6, we can add the deposit of R8,000 to the value calculated in (b). Using the same compound interest formula, the value of the deposit made at T1 at the end of T6 is R9,669.46.
(d) To calculate the value of the deposit made at T5 at the end of T6, we can add the deposit of R2,000 to the value calculated in (b). Using the same compound interest formula, the value of the deposit made at T5 at the end of T6 is R2,466.34.
(e) To determine the total value of the investment at the end of T6, we can sum up the values calculated in (b), (c), and (d). The total value of the investment at the end of T6 is R203,425.07.