Emiy F.

# interest rate question

Suppose one bank account pays 7% annual interest compounded once per year, and a second bank account pays 7% annual interest compounded continuously. If both bank accounts start with the same initial amount, how long will it take for the second bank account to contain twice the amount of the first bank account?

## 1 Expert Answer

By:

Andrew M. answered • 10/30/17

Tutor
New to Wyzant

Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors

Andrew M.

Sorry, didn't mean to hit "answer"... lol

Annual:  A = p(1.07)t     Continuous:  A = pe.07t

pe.07t = 2p(1.07)t
e.07t = 2(1.07)t
ln e.07t = ln[2(1.07)t]

.07t = ln 2 + ln 1.07t

.07t = ln 2 + 7 ln 1.07

t = [ln 2 + 7 ln 1.07]/.07

t = 16.667 years ...

approximately 16 2/3 years or 16 years 8 months

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10/30/17

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