The table above indicates the value of a $1500 investment at the end of each of the first four years. If this linear trend continues, how many years after the investment was made will its value be $3200?Table: Value after 1 year $1600, Value after 2 years $1700, Value after 3 years $1800, Value after 4 years $1900

Rationale

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

The investment shows a linear increase, and by analyzing the trend, we can determine the time it will take to reach $3200. Given the steady growth observed in the first four years, we can project this increase to find the year when the investment reaches the desired amount.

A (13) YOUR ANSWER

At 13 years, the value of the investment would be $2600, calculated by continuing the linear growth observed. This amount is insufficient relative to the target of $3200, indicating that 13 years is too early.

B (14) YOUR ANSWER

In 14 years, the investment's value would be $2700, again calculated using the linear trend. This is still below the target of $3200, confirming that this option does not meet the requirement.

C (16) YOUR ANSWER

If we project to 16 years, the investment would value $2900. While closer to the target, it still does not meet the $3200 goal, demonstrating that it requires more time to reach the desired amount.

D (17) CORRECT

After 17 years, the investment is projected to reach $3200. This is based on the established linear increase in value, confirming that this is indeed the correct answer as it aligns precisely with the target.

E (18) YOUR ANSWER

At 18 years, the value would be $3300, which exceeds the target of $3200. Therefore, reaching this amount in 18 years is unnecessary and incorrect.

Conclusion

The trend indicates that the investment grows linearly, and through careful calculation, we determined that it will take 17 years to reach a value of $3200. Options A, B, C, and E fail to meet the target amount either by being too early or exceeding it, while option D accurately reflects the necessary timeline for achieving the investment goal.

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

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