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# Exponential change

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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.

Guest Jul 14, 2017
edited by Guest  Jul 14, 2017
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#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
+84362
+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

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