Beth invests 6,329 in a savings account with a fixed annual interest rate of 3% compounded 3 times per year. How long will it take for the account balance to reach 7,131.68 3 years 4 years 6 years 5 years

To solve this problem, we can use the formula for compound interest: where:- is the amount of money accumulated after years, including interest.- is the principal amount (the initial amount of money).- is the annual interest rate (decimal).- is the number of times that interest is compounded per year.- is the time the money is invested for in years.Given:- - - - \( A = 7131.)We need to find .First, plug the given values into the formula: Simplify inside the parentheses: Next, divide both sides by 6329 to isolate the exponential term: To solve for , take the natural logarithm (ln) of both sides: Using the property of logarithms that \( \ln(a^b) = b \ln(a) \): Now, solve for : Calculate the values: So, Therefore, it will take approximately 4 years for the account balance to reach $7,131.68.The correct answer is:4 years