Question

Select ALL the correct answers.

Tammy deposits $1,850 in an individual retirement account earning 2.6% interest, compounded annually. She also deposits $2,015 in business interest bearing account earning 1.5% interest, compounded annually.

Select the equation and the number of years, x, it will take for the amount of money in both accounts to be equal. Round to the nearest whole year.

1,850(1.026)^x = 2,015(1.015)^x

1,850(1.26)^x = 2, 015(1.15)^x

1,850(1.126)^x = 2,015(1.115)^x

6 years

8 years

9 years

Answer 1

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.

Answer 2

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