Question
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R5 000 is invested in a bank that offers simple interest per annum and accumulates to R11 750 in 9 years. Calculate the rate of interest.

Ask by Ross Huff. in South Africa
Mar 13,2025

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Answer

The rate of interest is 15% per annum.

Solution

1. The amount accumulated with simple interest is given by \[ A = P(1 + rt) \] where \(P = 5000\) (principal), \(r\) is the rate of interest (in decimal form), and \(t = 9\) years. 2. Substitute the known values into the formula: \[ 11750 = 5000(1 + 9r) \] 3. Divide both sides by \(5000\) to isolate the term containing \(r\): \[ 1 + 9r = \frac{11750}{5000} = 2.35 \] 4. Subtract 1 from both sides to solve for \(9r\): \[ 9r = 2.35 - 1 = 1.35 \] 5. Divide both sides by \(9\) to find \(r\): \[ r = \frac{1.35}{9} = 0.15 \] 6. Convert \(r\) to a percentage: \[ 0.15 \times 100\% = 15\% \] Hence, the rate of interest is \(15\%\) per annum.

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To find the rate of interest, we can use the formula for simple interest: I = PRT, where I is the interest earned, P is the principal amount, R is the rate of interest per year, and T is the time in years. First, we calculate the interest earned: I = Total Amount - Principal I = R11,750 - R5,000 = R6,750. Now we can rearrange the formula to find R: 6,750 = 5,000 * R * 9. Solving for R gives us: R = 6,750 / (5,000 * 9) = 0.15 or 15%. So, the rate of interest is 15% per annum. You’ve just tackled a classic finance problem and calculated the rate of interest! Simple interest is prevalent in various saving accounts, making it easier than you think to keep track of your earnings. Many people appreciate the straightforwardness of this method instead of more complex compounding scenarios. Fun fact: The concept of simple interest dates back to ancient civilizations. The Babylonians and Egyptians used early forms of interest practices, laying the foundations for modern banking. Imagine how they calculated it without the fancy calculators we have today! Simple interest reminds us of how far we’ve come in understanding finance.

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