SOLUTION: How long will it take for $600 to grow to $26,600 at an interest rate of 6.2% if the interest is
compounded continuously? Round the number of years to the nearest hundredth.
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-> SOLUTION: How long will it take for $600 to grow to $26,600 at an interest rate of 6.2% if the interest is
compounded continuously? Round the number of years to the nearest hundredth.
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Question 1198521: How long will it take for $600 to grow to $26,600 at an interest rate of 6.2% if the interest is
compounded continuously? Round the number of years to the nearest hundredth. Found 3 solutions by Theo, MathTherapy, math_tutor2020:Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! continuous compounding formula is f = p * e ^ (r * t)
f is the future value
\p is the present value
e is the scientific constant of 2.710281828.....
r is the interest rate per year.
t is the number of years.
in your problem, the formula becomes:
26000 = 600 * e ^ (.062 * t)
divide both sides of the equaton by 600 to get:
26000/600 = e ^ (.062 * t)
take the natural log of both sides of the equation to get:
ln(26000/600) = ln(e ^ (.062 * t))
since ln(e ^ (.062 * t)) is equal to .062 * t ln(e) and .062 * t * ln(e) is equal to .062 * t because ln(e) is equal to 1, you get:
ln(26000/600) = .062 * t
solve for t to get:
t = ln(26000/600) / .062 = 60.78906713.
confirm by replacing 26000 with f and t with 60.7896713 to get:
f = 600 * e ^ (.062 * 60.7896713)
solve for f to get:
f = 26000.
this confirms the value of t is correct.
the natural log properties that allow this solution are:
ln(e^x) = x * ln(e)
ln(e) = 1
your solution is it would take 60.79 years for the value of 600 to grow to 26000 when the interest rate of 6.2% is compounded continuously.
You can put this solution on YOUR website! How long will it take for $600 to grow to $26,600 at an interest rate of 6.2% if the interest is
compounded continuously? Round the number of years to the nearest hundredth.
The person who responded is WRONG!
Formula for CONTINUOUS COMPOUNDING: ------ Converting to LOGARITHMIC (NATURAL) form
Time taken for $600 to grow to $26,600, or
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