How long will it take an investment of $7,000 to double if the investment earns interest at the rate of 8% compounded continuously?
Final Amount = Initial Amount x (1 + r)^t where r is the annual interest rate and t is the time in years.
Call the initial amount X, therefore the final amount will be 2X
Then, 2X = X(1+.08)^t
2 = (1.08)^t Now take the log of both sides
log(2) = log(1.08)^t = t log(1.08)
t = log(2) / log(1.08) = 9 years
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