Final answer:
The future cost of a home after 30 years with a 1% compounded continuously inflation rate is $371,211.02, calculated using the continuous compounding formula of Present Value multiplied by e raised to the rate times time.
Step-by-step explanation:
The student has asked to find the future cost of a home after 30 years, with a given inflation rate of 1% compounded continuously. The present value of the home is $275,000. To find the future value of the home, we can use the continuous compounding formula:
Future Value = Present Value * e^(rate*time)
Where e is the base of the natural logarithms (approximately equal to 2.71828), the rate is the annual inflation rate, and time is the number of years for which we are calculating the growth.
Plugging in the numbers:
Future Value = $275,000 * e^(0.01*30)
After calculating, we get:
Future Value = $275,000 * e^0.3
Future Value = $275,000 * 1.349858807576003
Future Value = $371,211.0223338008
After rounding to the nearest cent, the future value of the home will be $371,211.02.