You have $100 invested into an account that earns 5% interest compounded continuously. The future value of the account will be A = 100e^(.05t) in t years.
How long will it take for your $100 to double?
(Let A = 200) Solve for t
Round to one decimal.
1 Answer | Add Yours
The value of $100 invested in the account after t years is given by A = 100*e^(0.05*t).
Let T be the time taken for the amount to become double.
200 = 100*e^(0.05*T)
=> 2 = e^(0.05*T)
Take the natural logarithm of both the sides
ln 2 = ln(e^(0.05*T))
Use the property log a^b = b*log a and log_a a = 1
=> ln 2 = 0.05*T*1
=> T = (ln 2)/0.05
=> T `~~` 13.9
The amount in the account becomes double in 13.9 years.
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