Question
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5. If I invested R13 000 for 4 years and I now have R17 160, what was the simple interest rate given to me by the bank?

Ask by Little Allan. in South Africa
Feb 05,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

The simple interest rate is 8% per annum.

Solution

To determine the simple interest rate for your investment, you can use the **Simple Interest Formula**: \[ A = P(1 + rt) \] Where: - \( A \) = **Final Amount** (R17,160) - \( P \) = **Principal Amount** (R13,000) - \( r \) = **Annual Interest Rate** (as a decimal) - \( t \) = **Time** in years (4 years) **Step-by-Step Calculation:** 1. **Plug in the Known Values:** \[ 17,160 = 13,000 \times (1 + r \times 4) \] 2. **Divide Both Sides by 13,000 to Solve for \( (1 + 4r) \):** \[ \frac{17,160}{13,000} = 1 + 4r \] \[ 1.32 = 1 + 4r \] 3. **Subtract 1 from Both Sides to Isolate \( 4r \):** \[ 1.32 - 1 = 4r \] \[ 0.32 = 4r \] 4. **Divide Both Sides by 4 to Solve for \( r \):** \[ r = \frac{0.32}{4} \] \[ r = 0.08 \] 5. **Convert the Decimal to a Percentage:** \[ 0.08 \times 100 = 8\% \] **Conclusion:** The simple interest rate provided by the bank is **8% per annum**.

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Bonus Knowledge

To find the simple interest rate, you can use the formula for simple interest: \( A = P + I \), where \( A \) is the total amount, \( P \) is the principal amount, and \( I \) is the interest earned. In your case, \( A = R17,160 \) and \( P = R13,000 \), so the interest earned \( I = A - P = R17,160 - R13,000 = R4,160 \). Now, to find the interest rate \( r \), you can rearrange the interest formula: \( I = P \times r \times t \). Plugging in your values: \( R4,160 = R13,000 \times r \times 4 \). From here, you can solve for \( r \). Doing the math: \[ r = \frac{R4,160}{R13,000 \times 4} \] \[ r = \frac{R4,160}{R52,000} \] \[ r ≈ 0.08 \text{ or } 8\% \] So, the simple interest rate given to you by the bank is approximately 8%. To make calculations fun, remember that interest rates are like the icing on your financial cake. The more you understand how rates work, the more you can slice up your investments for a sweeter deal! Plus, it's like being a detective unraveled in numbers; each calculation leads you closer to the hidden treasure of understanding your money better!

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