Answer:
Step-by-step explanation:Let's break down the problem into two parts: the first investment for 3 years and the second investment for 5 years.
**First Investment (3 years):**
Given:
- Principal (\(P_1\)) = R2000
- Interest rate (\(r_1\)) = 10% or 0.10 (in decimal form)
- Time (\(t_1\)) = 3 years
The formula for calculating simple interest is:
\[I = P \times r \times t\]
Where:
- \(I\) = Interest earned
- \(P\) = Principal
- \(r\) = Interest rate
- \(t\) = Time
Calculate the interest earned (\(I_1\)) for the first investment.
**Second Investment (5 years):**
The initial amount plus interest earned (\(P_1 + I_1\)) from the first investment becomes the principal (\(P_2\)) for the second investment.
Given:
- Principal (\(P_2\)) = \(P_1 + I_1\)
- Interest rate (\(r_2\)) = 16% or 0.16 (in decimal form)
- Time (\(t_2\)) = 5 years
Calculate the interest earned (\(I_2\)) for the second investment.
**Total Value at the End of 8 Years:**
The total value at the end of 8 years will be the sum of the principal of the second investment and the interest earned from the second investment.
Calculate the total value at the end of 8 years.
Keep in mind that simple interest does not compound, so the interest earned each year remains constant.
Please perform the calculations for \(I_1\), \(I_2\), and the total value to find the final amount of the investment at the end of 8 years.