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Math  /  Algebra

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Edward purchased his home for $89,000\$ 89,000. For the first three years after he moved in, the real estate market was very lively, so his property value grew by 4.8%4.8 \% every year. For the next five years, the market slowed down somewhat, and his property value grew by 2.6%2.6 \% every year. How much had the value of Edward's home increased after eight years, to the nearest hundred dollars? a. $25,700\$ 25,700 b. $27,500\$ 27,500 c. $30,000\$ 30,000 d. $13,200\$ 13,200
Please select the best answer from the choices provided

Studdy Solution

STEP 1

1. Edward purchased his home for $89,000.
2. For the first three years, the property value increased by 4.8% each year.
3. For the next five years, the property value increased by 2.6% each year.
4. We need to find the increase in the value of Edward's home after eight years, rounded to the nearest hundred dollars.

STEP 2

1. Calculate the property value after the first three years.
2. Calculate the property value after the next five years.
3. Determine the total increase in property value.
4. Round the increase to the nearest hundred dollars and select the best answer.

STEP 3

Calculate the property value after the first three years.
The formula for compound interest is: V=P(1+r)t V = P(1 + r)^t
Where: - V V is the final value. - P P is the initial principal balance ($89,000). - \( r \) is the rate of interest per period (4.8% or 0.048). - \( t \) is the number of periods the money is invested for (3 years).
Substitute the values into the formula: V=89000(1+0.048)3 V = 89000(1 + 0.048)^3
Calculate: V≈89000×1.150≈102,350 V \approx 89000 \times 1.150 \approx 102,350

STEP 4

Calculate the property value after the next five years.
Now, use the new principal value ($102,350) and the new interest rate (2.6% or 0.026) for 5 years.
V=102350(1+0.026)5 V = 102350(1 + 0.026)^5
Calculate: V≈102350×1.136≈116,335 V \approx 102350 \times 1.136 \approx 116,335

STEP 5

Determine the total increase in property value.
Subtract the original purchase price from the final value: Increase=116,335−89,000=27,335 \text{Increase} = 116,335 - 89,000 = 27,335

STEP 6

Round the increase to the nearest hundred dollars and select the best answer.
Round 27,33527,335 to the nearest hundred dollars: Rounded Increase=27,300 \text{Rounded Increase} = 27,300
The closest option is: b. $27,500\$ 27,500

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