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Sara puts in 13 000$ in the account with the interest rate of 3.5%. How many years does it take before the amount has increased to 20 000$?

The answer is 13 years but I having some trouble finding how to solve the question. Please, I need some serious help.

Thanks in advance!

Guest Jul 14, 2017

edited by
Guest
Jul 14, 2017

#1**+1 **

FV = PV x [1 + R]^N

20,000 = 13,000 x [1 + 0.035]^N divide both sides by 13,000

1.53846..= 1.035^N Take the log of both sides

N =Log(1.53846...) / Log(1.035)

**N=12.52 ~ 13 Years.**

Guest Jul 14, 2017

#2**+1 **

20000 = 13000 (1 + .035)^{t} divide both sides by 13000

20/13 = (1 + .035)^{t}

20/13 = (1.035)^{t} take the log of both sides

log (20/13) = log (1.035)^{t} and we can write

log (20/13) = t * log (1.035) divide both sides by log (1.035)

log (20/13) / log (1.035) = t ≈ 12.52 years

CPhill Jul 14, 2017