To solve for the interest rate in this question, we will use the formula for simple interest. The formula for simple interest is:
[tex]\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \][/tex]
We are given:
- The principal amount ([tex]\( P \)[/tex]) is R 1800.
- The interest accrued ([tex]\( I \)[/tex]) is R 720.
- The time period ([tex]\( T \)[/tex]) is 5 years.
We need to find the rate of interest [tex]\( r \% \)[/tex] per annum.
Step-by-Step Solution:
1. Write the simple interest formula:
[tex]\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \][/tex]
[tex]\[ I = P \times r \times T \][/tex]
2. Rearrange the formula to solve for the rate ([tex]\( r \)[/tex]):
[tex]\[ r = \frac{I}{P \times T} \][/tex]
3. Substitute the given values into the formula:
- [tex]\( I = 720 \)[/tex]
- [tex]\( P = 1800 \)[/tex]
- [tex]\( T = 5 \)[/tex]
[tex]\[ r = \frac{720}{1800 \times 5} \][/tex]
4. Calculate the denominator:
[tex]\[ 1800 \times 5 = 9000 \][/tex]
5. Substitute the result back into the equation:
[tex]\[ r = \frac{720}{9000} \][/tex]
6. Simplify the fraction:
[tex]\[ r = \frac{720}{9000} = 0.08 \][/tex]
7. Convert the rate to a percentage by multiplying by 100:
[tex]\[ r \times 100 = 0.08 \times 100 = 8\% \][/tex]
So, the interest rate is [tex]\( 8\% \)[/tex] per annum.
