SOLUTION: Bob is surprised. An ancestor deposited $20.00 in a savings account. The annual rate is 4% compounded continuously. Bob is inheriting $32,000. In what year was the account opened i

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Bob is surprised. An ancestor deposited $20.00 in a savings account. The annual rate is 4% compounded continuously. Bob is inheriting $32,000. In what year was the account opened i      Log On


   

Question 1096037: Bob is surprised. An ancestor deposited $20.00 in a savings account. The annual rate is 4% compounded continuously. Bob is inheriting $32,000. In what year was the account opened if Bob is inheriting this year ?
Found 3 solutions by addingup, MathTherapy, ikleyn:
Answer by addingup(3677) About Me  (Show Source):
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32,000 = 20e^(0.04t)
e^(0.04t) = 1600
log(e^(0.04)t) = log(1600}
0.04t = log(1600)
t = log(1600)/0.04 = 80.1 years

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!
Bob is surprised. An ancestor deposited $20.00 in a savings account. The annual rate is 4% compounded continuously. Bob is inheriting $32,000. In what year was the account opened if Bob is inheriting this year ? 
80+ YEARS is INCORRECT/WRONG/INACCURATE.

Correct answer: highlight_green%28matrix%281%2C5%2C+184.44%2C+years%2C+before%2C+this%2C+year%29%29

Answer by ikleyn(52921) About Me  (Show Source):
You can put this solution on YOUR website!
.
Bob is surprised. An ancestor deposited $20.00 in a savings account. The annual rate is 4% compounded continuously.
Bob is inheriting $32,000. In what year was the account opened if Bob is inheriting this year ?
~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

32000 = 20*e^(0.04*t),  ====>


e^(0.04*t) = 32000%2F20 = 3200%2F2 = 1600  ====>


0.04*t = ln(1600)  ====>  t = %281%2F0.04%29%29*ln(1600) = 184.44 years.