2300 dollars is placed in an account with an annual interest rate of 5.5%. To the nearest tenth of a year, how long will it take for the account value to reach 4300 dollars?

Answer 1

Let t be the number of years it takes for the account value to reach 4300 dollars. We know that 2300*(1+5.5/100)^t = 4300.
The equation above simplifies to 1.055^t = 1.8695652173913042.
Taking the natural log of both sides, we get t*ln(1.055) = ln(1.8695652173913042).
Dividing both sides by ln(1.055), we get t = ln(1.8695652173913042)/ln(1.055).
Calculating ln(1.8695652173913042)/ln(1.055), we get t to be approximately 11.4.
Therefore, it will take approximately 11.4 years for the account value to reach 4300 dollars. Answer: \boxed{11.4}.