We can write the equation for the amount of money after x years in Tammy's individual retirement account as 1850(1+0.026)^x
and the equation for the amount of money after x years in Tammy's business interest bearing account as 2015(1+0.015)^x
We equate the above expressions to find the number of years x it will take for the amount of money in both accounts to be equal: 1850(1+0.026)^x = 2015(1+0.015)^x 1850(1.026)^x = 2015(1.015)^x <--this is our first answer (1.026)^x / (1.015)^x = 2015 / 1850 (1.026 / 1.015)^x = 2015 / 1850
Taking the log of both sides of our equation, x log (1.026/1.015) = log (2015/1850)
number of years x is x = log (2015/1850) / log (1.026/1.015) x = 7.926 ≈ 8 years
Income of the first account after x years: Income of the second account after x years: Equating the above tw values we get the equation: Solving the above equation for x: Answer 8 years.