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The investment will reach a value of $3200 in 17 years.

Based on the linear trend observed in the provided table, the value of the investment increases by $100 each year. To determine when the investment will reach $3200, we can calculate the number of years required from the value of $1900 at the end of year 4.

A) 13

Choosing 13 years suggests that the investment would reach $3200 much too early, as it would only allow for a total increase of $1300 from the original $1500 investment. This would place the value at $2800, which is significantly less than the target value of $3200.

B) 14

Selecting 14 years would mean the investment value would be $2900, calculated from the baseline of $1900 at year 4, plus an additional $100 for each of the next 10 years. This still falls short of the target of $3200.

C) 16

A choice of 16 years would yield a value of $3100, as the investment would be worth $1900 at year 4 plus $1200 over the next 12 years. This value is still below the required $3200, making this option incorrect.

D) 17

In 17 years, the investment value would reach $3200. Starting from $1900 at year 4, adding $1300 over the next 13 years results in exactly $3200, confirming that this option is correct.

E) 18

Choosing 18 years would indicate a value of $3300, which exceeds the target of $3200. This makes the option incorrect, as it does not accurately reflect the investment's growth trajectory.

Conclusion

The correct answer is 17 years, as this aligns perfectly with the calculated value of $3200 based on the linear increase of $100 per year. All other options either fall below or exceed this target, demonstrating their incorrectness in the context of the investment's growth.