Question
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c. Lauren invests R3 500 at \( 4,5 \% \) p.a. simple interest. After a certain amount of years, it grew to R 4602,50 . Calculate the number of years it took to grow to R 4602,50. A. 5 B. 6 C. 7 D. 8.

Ask by Wright Hammond. in South Africa
Nov 04,2024

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Answer

The number of years it took for the investment to grow to R4,602.50 is 7 years.

Solution

To find the number of years it took for Lauren's investment to grow from R3,500 to R4,602.50 at a simple interest rate of 4.5% per annum, we can use the formula for simple interest: \[ A = P(1 + rt) \] Where: - \( A \) is the final amount (R4,602.50) - \( P \) is the principal amount (R3,500) - \( r \) is the rate of interest (4.5% or 0.045) - \( t \) is the time in years We can rearrange the formula to solve for \( t \): \[ t = \frac{A - P}{Pr} \] Now, substituting the values into the formula: \[ t = \frac{4602.50 - 3500}{3500 \times 0.045} \] Calculating the numerator: \[ 4602.50 - 3500 = 1102.50 \] Calculating the denominator: \[ 3500 \times 0.045 = 157.5 \] Now, substituting these values back into the equation for \( t \): \[ t = \frac{1102.50}{157.5} \approx 7 \] Thus, the number of years it took for the investment to grow to R4,602.50 is approximately 7 years. The answer is **C. 7**.

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The Deep Dive

To determine how many years it took for Lauren's investment to grow from R3,500 to R4,602.50 using simple interest, you can use the formula for simple interest: \[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \] First, calculate the interest earned: \[ \text{Interest} = R4602.50 - R3500 = R1102.50 \] Rearranging the formula to solve for time (T) gives: \[ T = \frac{\text{Interest}}{\text{Principal} \times \text{Rate}} \] Substituting the values: \[ T = \frac{1102.50}{3500 \times 0.045} \] \[ T = \frac{1102.50}{157.5} \approx 7 \] The duration it took for Lauren's investment to grow to R4,602.50 is **7 years** (C). You got it right! Always remember that small investments, when nurtured with patience, can produce fruitful results over time! Speaking of patience, did you know that Albert Einstein once said, “Compound interest is the eighth wonder of the world?” Well, while this question involves simple interest, it's a great reminder to explore the difference between the two! Both forms of interest have their unique advantages.

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