SOLUTION: If I want to invest 10,000 dollars, how long will it take to double my investment at an annual interest rate of 10 percent, compounded continuously?

Question 1034117: If I want to invest 10,000 dollars, how long will it take to double my investment at an annual interest rate of 10 percent, compounded continuously?
Found 2 solutions by robertb, Theo:
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!

Let A = 20,000.
==> ==> ==> years, to three significant figures.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
continuous compound formula is f = p * e^(rn)

f is the future value
p is the present value
r is the interest rate per time period.
n is the number of time periods.

if you want to double your investment, then f = 20,000 and p = 10,000.
your annual interest rate is .10 (percent / 100 = rate).

formula becomes 20,000 = 10,000 * e^(.1*n)

divide both sides of this equation by 10,000 to get 2 = e^(.1*n).
take the natural log of both sides of this equation to get ln(2) = ln(e^(.1*n)).
since ln(e^.1*n) = .1*n*ln(e), and since ln)(e) = 1, your equation becomes ln(2) = .1*n.
divide both sides of this equation by .1 to get ln(2)/.1 = n
solve for n to get n = ln(2)/.1 = 6.931471806.

i will take 6.931471806 year to double your money at 10% interest rate per year.

replace n in your original equation to get 20,000 = 10,000 * e^(.1*6.931471806) which results in 20,000 = 20,000.
this confirms the solution is correct.

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