Final answer:
The cost of the home in 30 years, assuming an inflation rate of 1% compounded continuously, would be approximately $363,164.58.
Step-by-step explanation:
To find the cost of a home in 30 years, assuming an inflation rate of 1% (compounded continuously) and a present value of $225,000, we can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
- A is the future value (cost of the home)
- P is the present value ($225,000)
- e is Euler's number (approximately 2.71828)
- r is the interest rate (1% or 0.01)
- t is the time in years (30)
Substituting the values into the formula, we get:
A = $225,000 * e^(0.01 * 30)
Calculating this value, we find that the cost of the home in 30 years will be approximately $363,164.58.