Question

Karen makes bad investment choices. She invested $250,000 in a food truck right before spring break in March 2020. The business has lost 13.5% of its total valuation every month. How much is her investment worth now after 8 months?

a) $29,908.40
b) $33,750
c) $78,355.39
d) $206,680.39

Answer 1

Karen's investment value after 8 months, given a monthly loss of 13.5%, can be calculated using exponential decay. The final value of her investment is $78,355.39.

Step-by-step explanation:

The student's question is about determining the value of an investment after a continuous loss. To calculate the current value of Karen's investment after 8 months with a monthly loss of 13.5%, we can use the formula for exponential decay, which is:

Final Value = Initial Value × (1 - Rate of Loss)^Number of Periods

Where the Initial Value is $250,000, the Rate of Loss is 13.5% or 0.135, and the Number of Periods is 8 months.

Plugging in the values:

Final Value = $250,000 × (1 - 0.135)^8

Final Value = $250,000 × (0.865)^8

Final Value = $250,000 × 0.316242

Final Value = $78,355.39

Karen's investment is worth $78,355.39 after 8 months, which corresponds to option