Sam knows that his annual homeowners insurance premium is $0.27 per $100 of value, which usually works out to be $683.10 annually. But Sam is confused by a letter from his insurance company telling him that an increase in the value of his home has led to an increase in his annual homeowners insurance premium. He is now being charged an annual premium of $720.90. Based on the increase in his annual homeowners insurance premium, what was the increase in his home's value? (Note: The cost is still $0.27 per $100, even though the annual premium went up.)

Question

a.
$140
b.
$1,400
c.
$14,000
d.
$140,000

Answer 1

To determine the increase in Sam's home's value based on the change in his annual homeowners insurance premium, we can follow these steps:

1. Calculate the original value of Sam's home using the original annual premium: $$\text{Original Premium}=683.10$$ Since the premium is $0.27 per $100 of home value, we can express this as: $$\text{Home Value}=\frac{\text{Original Premium}}{0.27}\times 100$$ $$\text{Home Value}=\frac{683.10}{0.27}\times 100\approx 25300$$

2. Calculate the new value of Sam's home using the new annual premium: $$\text{New Premium}=720.90$$ Using the same method: $$\text{New Home Value}=\frac{\text{New Premium}}{0.27}\times 100$$ $$\text{New Home Value}=\frac{720.90}{0.27}\times 100\approx 26700$$

3. Calculate the increase in home value: $$\text{Increase in Home Value}=\text{New Home Value}-\text{Original Home Value}$$ $$\text{Increase in Home Value}=26700-25300=1400$$

Thus, the increase in Sam's home's value is $1,400.

The answer is (b) $1,400.