Instructions: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.

Question

02-04-2018
Mathematics

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Instructions: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.

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jadacarter1603 jadacarter1603 · Answer 1 · 2018-04-04T17:34:00+02:00

First account:P = $1850, the principalr = 2.6%, the interest raten = 1, the compounding interval
Second account:P = $2015r = 1.5%n = 1
Let x = the number of years for both accounts to attain the same value.Then1850(1 + 0.026)ˣ = 2015(1 + 0.015)ˣ1.026ˣ = 1.0892(1.015ˣ)(1.026/1.015)ˣ = 1.08921.0108ˣ = 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 yrs