You invest $6000 at an annual interest of 3% compounded continuousl. How long will it take in years to double and then triple your money?

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Answer 1 · 2017-11-27T05:35:16

Double in #~=23.1#yrs, Triple in #~=36.6#yrs

The amount accumulated #(Q_t)# from a principal of #P# at #r%# per period after #t# periods compounded continuously is given by:

#Q_t = Pxx e^((rt)/100)#

i.e. #Q_t /P = e^((rt)/100)#

In this example, the actual principal amount #($6,000)# is irrelevant as to double any principal amount, #Q_t /P = 2#

#:.# to double an amount at 3% p.a. compounded continuously.

#e^(0.03t) = 2#

#0.03t = ln2#

#t approx 0.6931/0.03 approx 23.1#yrs

To check result using the principal $6,000

#Q_23.1 = 6,000 xx e^(0.03xx23.1) approx 11998 approx 12,000#

Similarly, to triple a principal amount at 3% p.a. compounded continuously.

#0.03t = ln3#

#t approx 1.0986/0.03 approx 36.6#yrs

Again to check using #P=6,000#:

#Q_36.6 = 6,000 xx e^(0.03xx36.6) approx 17989approx 18,000#