To find the rate of interest per annum where a principal amount of R 640 grows to R 740.80 in 3 years, we can use the formula for simple interest.
The formula to calculate the amount in simple interest is:
[tex]\[ A = P(1 + rt) \][/tex]
Where:
- [tex]\( A \)[/tex] is the final amount (R 740.80 in this case)
- [tex]\( P \)[/tex] is the principal amount (R 640 in this case)
- [tex]\( r \)[/tex] is the annual interest rate (the rate we need to find)
- [tex]\( t \)[/tex] is the time in years (3 years in this case)
We can rearrange this formula to solve for [tex]\( r \)[/tex]:
[tex]\[ r = \frac{A/P - 1}{t} \][/tex]
First, substitute the values we have:
[tex]\[ r = \frac{740.80 / 640 - 1}{3} \][/tex]
Now calculate the intermediate steps:
1. Calculate [tex]\( \frac{740.80}{640} \)[/tex]:
[tex]\[ \frac{740.80}{640} = 1.1575 \][/tex]
2. Subtract 1 from this value:
[tex]\[ 1.1575 - 1 = 0.1575 \][/tex]
3. Divide this result by the number of years (3):
[tex]\[ \frac{0.1575}{3} = 0.0525 \][/tex]
4. Convert this decimal to a percentage by multiplying by 100:
[tex]\[ 0.0525 \times 100 = 5.25 \% \][/tex]
Therefore, the rate of interest per annum that will cause R 640 to amount to R 740.80 in 3 years is approximately 5.25%.
