Question

Select ALL the correct answers.

Answer 1

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

Answer 2

Income of the first account after x years:
$1,850(1.026)^x$
Income of the second account after x years:
$2,015(1.015)^x$
Equating the above tw values we get the equation:
$1,850(1.026)^x=2,015(1.015)^x$
Solving the above equation for x:
$x=8$
Answer 8 years.