Question

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.

Answer 1

First account:
P = $1850, the principal
r = 2.6%, the interest rate
n = 1, the compounding interval

Second account:
P = $2015
r = 1.5%
n = 1

Let x = the number of years for both accounts to attain the same value.
Then
1850(1 + 0.026)ˣ = 2015(1 + 0.015)ˣ
1.026ˣ = 1.0892(1.015ˣ)
(1.026/1.015)ˣ = 1.0892
1.0108ˣ = 1.0892

Take logarithms of both sides.
x ln(1.0108) = ln(1.0892)
x = ln(1.0854)/ln(1.0108) = 7.95 ≈ 8 years

Answer: 8 years