Kate L.

asked • 11/02/16# How long will it take for an investment of $1,000 to double in value if the interest rate is 7.5% per year, compounded continuously?

I'm doing test corrections for my pre-cal class and Ive got the answer (9.24 years) i just need to know how to get there because I used the wrong equation the first time (2000=1000e^7.5t).

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## 1 Expert Answer

Andrew M. answered • 11/02/16

Tutor

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

**A = Pe**is formula for continuously compounded interest

^{rt }A = final amount = 2000

P = principal = 1000

e = euler's number (on calculator)

r = interest rate as decimal = .075

t = time in years

Your mistake is that 7.5% as a decimal is 7.5/100 = .075

not 7.5

2000 = 1000e

^{.075t}e

^{.075t}= 2000/1000e

^{.075t}= 2take natural log of both sides

ln e

^{.075t}= ln 2.075t = ln 2

t = ln2/.075

t = 9.24 years

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Mark M.

11/02/16