How long will it take for an investment of $3,000 to double if the investment earns interest at the rate of 4%/year compounded continuously? (Round your answer to one decimal place.)

Question

How long will it take for an investment of $3,000 to double if the investment earns interest at the rate of 4%/year compounded continuously? (Round your answer to one decimal place.)

__________yr

Answer 1

P(t) = 3,000e^.04t

6,000 = 3,000e^.04t

2 = e^.04t

ln2 = .04t

t ~ 17 yrs

For continuous interest, the doubling time formula, t = ln2 / r , is an easy and useful one to remember. Notice that it is completely independent of the initial value (as is doubling time for exponential growth at any rate).

For annual interest compounded once per year, we also have an approximation called "the rule of 72" which gives us the approximate doubling time as 72/r when r is expressed as a percent rather than a decimal.