Question
Omari buys a house for \( £ 190,000 \). The value of the house appreciates by \( 5.1 \% \) every year. How much is the house worth after 6 years? Round your answer to the nearest penny.
Ask by Blake Chandler. in Egypt
Jan 21,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
After 6 years, the house is worth approximately £256,076.38.
Solution
To determine the future value of Omari's house after 6 years with an annual appreciation rate of \(5.1\%\), we can use the compound interest formula:
\[
A = P \times (1 + r)^t
\]
Where:
- \(A\) = future value of the house
- \(P\) = initial purchase price (\(£190,000\))
- \(r\) = annual appreciation rate (\(5.1\% = 0.051\))
- \(t\) = number of years (6)
Plugging in the values:
\[
A = 190,000 \times (1 + 0.051)^6
\]
\[
A = 190,000 \times (1.051)^6
\]
First, calculate \((1.051)^6\):
\[
(1.051)^6 \approx 1.34777
\]
Now, multiply this by the initial price:
\[
A = 190,000 \times 1.34777 \approx £256,076.38
\]
**Answer:** After 6 years, the house is worth approximately £256 076.38.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To find out how much the house is worth after 6 years with an annual appreciation of 5.1%, we can use the formula for compound interest: \[ A = P(1 + r)^n \] Where: - \( A \) is the amount of money accumulated after n years, including interest. - \( P \) is the principal amount (the initial amount of money). - \( r \) is the annual interest rate (decimal). - \( n \) is the number of years. Plugging in the values: - \( P = 190,000 \) - \( r = 0.051 \) - \( n = 6 \) \[ A = 190,000(1 + 0.051)^6 \] \[ A = 190,000(1.051)^6 \] \[ A = 190,000 \times 1.348850268 \] \[ A \approx 256,282.32 \] Therefore, the house is worth approximately \( £256,282.32 \) after 6 years.
