SOLUTION: I need help solving this problem. A man invests $7000 in an account that pays 7% interest per year, compounded continuously. How long will it take for the amount to be $8500?

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Question 291554: I need help solving this problem.
A man invests $7000 in an account that pays 7% interest per year, compounded continuously. How long will it take for the amount to be $8500?
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
$7000 invested at 7% interest per year compounded continuously.
How long to make it $8500?

Continouos compounding formula is F = P *

F = future value = $8500
P = present value = $7000
i = annual interest rate = .07
n = number of years = what you are trying to find.
e = scientific constant = 2.718281828...

Replace know values in this equation to get:

8500 = 7000 *

Divide both sides of this equation by 7000 to get:

=

Simplify to get:

1.214285714 =

Take the natural log of both sides of this equation to get:

ln(1.214285714 = ln()

Since ln() = n*ln(x), your equation becomes:

ln(1.214285714) = .07*n*ln(e)

Since ln(e) = 1, your equation becomes

ln(1.214285714) = .07*n

Divide both sides of this equation by .07 to get:

ln(1.214285714)/.07 = n

Simplify by getting ln(1.214285714) to get:

.194156014 / .07 = n

Simplify further to get:

n = 2.773657349

Your $7000 investment should grow to $8500 in 2.773657349 years.

Confirm by substituting 2.773657349 for n in your original equation to get:

$8500 = $7000 * .

Simplify to get:

$8500 = $8500 confirming that the value for n of 2.773657349 is good.

Your answer is that your $7000 will grow to $8500 in 2.773657349 years assuming continuous compounding at an annual interest rate of 7% per year.