Sure, let's walk through the given questions step-by-step.
### Question 2.1.1
Calculate the total amount that the learners will have at the end of two years if they chose Option One.
Option One involves compound interest where the principal amount [tex]\( P = R3800 \)[/tex], the annual interest rate [tex]\( r = 0.05 \)[/tex], and the time period is [tex]\( t = 2 \)[/tex] years. The compound interest formula is:
[tex]\[ A = P (1 + r)^t \][/tex]
Substitute the values into the formula:
[tex]\[ A = 3800 \times (1 + 0.05)^2 \][/tex]
[tex]\[ A = 3800 \times (1.05)^2 \][/tex]
[tex]\[ A = 3800 \times 1.1025 \][/tex]
[tex]\[ A = 4189.5 \][/tex]
So, the total amount after two years if they chose Option One is R4189.5.
### Question 2.1.2
Calculate the missing values A and B in the given table for Option Two.
The table shows the initial amount, interest earned, and final amount for each year.
For Year 1:
- Initial amount is R3800
- Final amount is R3971
- Interest earned (A) is calculated as follows:
[tex]\[ A = 3971 - 3800 \][/tex]
[tex]\[ A = 171 \][/tex]
Therefore, the interest earned in Year 1 (A) is R171.
For Year 2:
- Initial amount is R3971
- Interest earned is R178.895
- Final amount (B) is calculated as follows:
[tex]\[ B = 3971 + 178.895 \][/tex]
[tex]\[ B = 4149.895 \][/tex]
Therefore, the final amount at the end of Year 2 (B) is R4149.895.
### Question 2.1.3
Which was a better option for investing the money, and why?
To determine the better option, we compare the total amounts at the end of the two years for both options.
- Total amount for Option One: R4189.5
- Total amount for Option Two: R4149.895
Clearly, Option One gives a greater return because R4189.5 is more than R4149.895.
Hence, the better option for investing the money is Option One because it yields a higher total return after two years.
