SOLUTION: If you invest $2,500 in an account, what is the time that will take you to get $2,571 if the interest rate is 0.7% compounded continuously?

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Question 1159783: If you invest $2,500 in an account, what is the time that will take you to get $2,571 if the
interest rate is 0.7% compounded continuously?
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
the continuous compounding formula is f = p * e ^ (r * t)
f is the future value.
p is the present value.
r is the interest rate per time period.
t is the number of time periods.

in this problem, the time period is in years and the formula becomes:
2571 = 2500 * e ^ (.007 * t)

the formula says that 2500 becomes 2571 in t years at the rate of .007 per year.

in this formula, you are using the rate rather than the rate percent.
the rate is equal to the rate percent divided by 100.
that makes r = .7% / 100 = .007.

divide both sides of this formula by 2500 to get:
2571 / 2500 = e ^ (.007 * t)
take the natural log of both sides of this equation to get:
ln(2571/2500) = ln(e^(.007*t)).
since ln(e^(.007*t)) is equal to t * ln(e^(.007)), the formula becomes:
ln(2571/2500) = t * ln(e^(.007)).
solve for t to get:
t = ln(2571/2500) / ln(e^(.007)) = 4.000599487 years.

to confirm, replace t in the original equation with that to get:
2571 = 2500 * e^(.007 * 4.000599487) = 2571.
the solution is confirmed to be good.
the solution is that 2500 will become 2571 in 4.000599487 years at the rate of .7% per year compounded continuously.



Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

If you invest $2,500 in an account, what is the time that will take you to get $2,571 if the
interest rate is 0.7% compounded continuously?


 ----- Making necessary substitutions



 ------ Converting to EXPONENTIAL form

Time for $2,500 to accumulate to $2,571, or 

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