What would it cost an insurance company to replace a family’s personal property that originally cost $50,000? The replacement costs for the items have increased 18 percent.
The correct answer and explanation is:
Answer:
To find the cost to replace the family’s personal property after an 18% increase in replacement costs, we calculate: Replacement Cost=Original Cost+(Original Cost×Increase Percentage)\text{Replacement Cost} = \text{Original Cost} + (\text{Original Cost} \times \text{Increase Percentage}) =50,000+(50,000×0.18)=50,000+9,000=59,000= 50,000 + (50,000 \times 0.18) = 50,000 + 9,000 = 59,000
So, it would cost the insurance company $59,000 to replace the family’s personal property.
Explanation (300 words):
When an insurance company considers the cost to replace a family’s personal property, they look at the current market value required to buy new items of similar kind and quality—not the original purchase price. This is known as the replacement cost. Over time, the prices of goods typically increase due to factors such as inflation, changes in supply and demand, or manufacturing costs. This increase is often expressed as a percentage.
In this scenario, the original value of the family’s personal property was $50,000. The replacement cost has increased by 18%, which means the current price to purchase the same quality and quantity of items is higher than it was originally.
To calculate the new replacement cost, we multiply the original cost by the percentage increase (expressed as a decimal), then add this amount to the original cost. Mathematically, this is: New Replacement Cost=Original Cost×(1+Percentage Increase)\text{New Replacement Cost} = \text{Original Cost} \times (1 + \text{Percentage Increase})
Here, the percentage increase is 18%, or 0.18 in decimal form. 59,000=50,000×(1+0.18)59,000 = 50,000 \times (1 + 0.18)
This calculation tells the insurance company how much they would need to pay if the family lost all their personal property and needed to replace everything today.
Understanding replacement cost is important because if the insurance coverage is based only on the original purchase price without considering inflation or increased costs, the family may be underinsured. This could result in a payout that’s insufficient to fully replace lost items.
In summary, the insurance company would need $59,000 to replace the family’s personal property reflecting the 18% increase in replacement costs. This ensures the family is compensated fairly according to current market prices.