Sure, let's break this down step-by-step.
Moses decides to invest his bonus of R8,000 at a simple interest rate of 6% for 5 years. We will use the simple interest formula to find out how much his investment will be after 5 years.
The simple interest formula is:
[tex]\[ A = P(1 + i \cdot n) \][/tex]
Where:
- [tex]\( A \)[/tex] is the amount of money accumulated after n years, including interest.
- [tex]\( P \)[/tex] is the principal amount (the initial amount of money).
- [tex]\( i \)[/tex] is the annual interest rate (as a decimal).
- [tex]\( n \)[/tex] is the number of years the money is invested or borrowed for.
Given values:
- [tex]\( P = \text{R} 8,000 \)[/tex]
- [tex]\( i = 0.06 \)[/tex] (6% as a decimal)
- [tex]\( n = 5 \)[/tex] years
Substitute these values into the formula:
[tex]\[ A = 8000 \left( 1 + 0.06 \cdot 5 \right) \][/tex]
First, calculate the term inside the parenthesis:
[tex]\[ 1 + 0.06 \cdot 5 = 1 + 0.30 = 1.30 \][/tex]
Now multiply this by the principal amount:
[tex]\[ A = 8000 \times 1.30 \][/tex]
This gives us the final amount:
[tex]\[ A = 10400 \][/tex]
Therefore, Moses's investment will be R10,400 after 5 years.
