Question 207830: In algebra, if I have $2,938.70, how long will it take to double my money at 8% interest rate and contiunuous compounding?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! additional information can be found at: http://cs.selu.edu/~rbyrd/math/continuous/
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present value is $2,938.70
interest rate = 8% per year with continuous compounding.
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formula is:
FV = PV * e^(r*t)
where:
FV = future value
PV = present value
e = napier's constant
r = annual interest rate
t = number of years
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your problem asks for how many years which makes the formula become:
2*(2938.70) = 2938.70 * e^(.08*t)
we're solving for t.
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divide both sides of this equation by 2938.70 to get:
2 * (2938.70) / (2938.70) = e^(.08*t)
formula becomes:
2 = e^(.08*t)
take the log of both sides of this equation to get:
log(2) = log(e^(.08*t))
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by the laws of logarithms, this becomes:
log(2) = (.08*t) * log(e)
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this becomes:
.08*t = log(2)/log(e) which becomes:
t = (log(2)/log(e))/(.08) which becomes:
t = 8.664339757 years.
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we can plug this value into the original equation to see if it's accurate.
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2 = e^(.08*t) becomes:
2 = e^(.08*8.664339757) which becomes:
2 = 2 confirming the value calculated is correct according to the formula.
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as a comparison, with monthly compounding, the money will double in 8.693188906 years.
with daily compounding, the money will double in 8.665289239 years.
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