Final answer:
The value of Jim's house at the end of 2017, after a 5% annual increase from an initial value of £240,000, would be approximately £291734.50.
Step-by-step explanation:
To calculate the value of Jim's house at the end of 2017 after a 5% annual increase from the start of 2014, we'll use the compound interest formula without the addition of periodic contributions since we're only considering the appreciation in the house value, not recurring investments. To simplify the calculation, we can treat this as a compound interest problem with the initial principal amount (£240,000), an annual interest rate (5%), and a compounding period of 4 years (from 2014 to 2017).
The compound interest formula is:
Final Value = Principal × (1 + Rate)^n
Where:
- Principal is the initial value of the house (£240,000)
- Rate is the annual increase rate (5% or 0.05)
- n is the number of years the value is compounding (4 years)
Now, we calculate:
Final Value = £240,000 × (1 + 0.05)^4
Final Value = £240,000 × (1.05)^4
Final Value = £240,000 × 1.21550625
Final Value = £291734.50
The house's value at the end of 2017 would be approximately £291734.50.