Haynes Potter
05/28/2023 · Junior High School
64. At what simple interest rate will R4 500 increase to R6 000 in 2 years and 8 months?
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Step-by-step Solution
To find the simple interest rate, we can use the formula for simple interest:
\[
A = P(1 + rt)
\]
Where:
- \( A \) is the final amount (R6,000)
- \( P \) is the principal amount (R4,500)
- \( r \) is the interest rate (as a decimal)
- \( t \) is the time in years
First, we need to convert the time from years and months into years.
2 years and 8 months can be converted as follows:
\[
t = 2 + \frac{8}{12} = 2 + \frac{2}{3} = \frac{6}{3} + \frac{2}{3} = \frac{8}{3} \text{ years}
\]
Now we can substitute the values into the formula:
\[
6000 = 4500(1 + r \cdot \frac{8}{3})
\]
Next, we can solve for \( r \):
1. Divide both sides by 4500:
\[
\frac{6000}{4500} = 1 + r \cdot \frac{8}{3}
\]
\[
\frac{4}{3} = 1 + r \cdot \frac{8}{3}
\]
2. Subtract 1 from both sides:
\[
\frac{4}{3} - 1 = r \cdot \frac{8}{3}
\]
\[
\frac{4}{3} - \frac{3}{3} = r \cdot \frac{8}{3}
\]
\[
\frac{1}{3} = r \cdot \frac{8}{3}
\]
3. Multiply both sides by \(\frac{3}{8}\):
\[
r = \frac{1}{3} \cdot \frac{3}{8} = \frac{1}{8}
\]
4. Convert \( r \) to a percentage:
\[
r = \frac{1}{8} = 0.125 \text{ or } 12.5\%
\]
Thus, the simple interest rate is **12.5%**.
Quick Answer
The simple interest rate is 12.5%.
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