To estimate the balance of the investment after 15 years, we first need to understand how the investment grows.
Given that the principal is $5,000 and it increases by 70% every 10 years, we can calculate the amount after 10 years:
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Calculate the amount after 10 years:
- The increase is 70% of $5,000, which can be calculated as follows: \[ 70% \text{ of } 5000 = 0.70 \times 5000 = 3500 \]
- Therefore, the total amount after 10 years is: \[ 5000 + 3500 = 8500 \]
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Calculate the amount after another 5 years:
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To estimate the balance after 15 years, we can find the annual growth rate based on the principal amount of $5,000 increasing to $8,500 over 10 years.
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The growth from $5,000 to $8,500 constitutes a growth factor of: \[ \text{Growth factor after 10 years} = \frac{8500}{5000} = 1.7 \]
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The annual growth rate (r) can be determined using the formula for compound growth: \[ (1 + r)^{10} = 1.7 \]
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Taking the 10th root: \[ 1 + r \approx 1.7^{(1/10)} \]
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Using a calculator: \[ r \approx 1.0547 \text{ (approximately)} \]
This indicates an annual growth rate of about 5.47%.
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Calculate the total amount after 15 years:
- Since we have already computed the amount after 10 years as $8,500, we can compute the amount for the additional 5 years: \[ \text{Amount after 15 years} = 8500 \times (1 + r)^5 \] \[ = 8500 \times (1.0547)^5 \]
- Calculating \((1.0547)^5\) using a calculator: \[ (1.0547)^5 \approx 1.302 \]
- Therefore: \[ \text{Amount after 15 years} \approx 8500 \times 1.302 \approx 11067 \]
Finally, rounding to the nearest thousand, the estimated balance of the investment after 15 years is approximately $11,000.
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