To determine the future value of the painting after 70 years, given that it increases in value by a factor of 1.2 each year, you can use the formula for exponential growth:
\[ \text{Future Value} = \text{Present Value} \times (\text{growth factor})^{\text{number of years}} \]
In this case:
- Present Value = $135
- Growth factor = 1.2
- Number of years = 70
Plugging in the values:
\[ \text{Future Value} = 135 \times (1.2)^{70} \]
Now, calculate \( (1.2)^{70} \):
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Calculate the exponent: \( 1.2^{70} \approx 169.175 \) (this can be calculated using a scientific calculator or software)
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Now, multiply that result by the present value:
\[ \text{Future Value} \approx 135 \times 169.175 \approx 22839.125 \]
Therefore, the painting will be worth approximately $22,839.13 after 70 years.
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