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.

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.

Answer by MathTherapy(10555)   (Show Source): 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

Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

The tutor @Theo has made a typo.

He wrote
t = ln(26000/600) / .062 = 60.78906713

when it should be
t = ln(26600/600) / .062 = 61.1570458

The 26000 should be 26600

That then rounds to 61.16 to be the final answer.

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