Carl plans to invest $500 at 8.25% interest, compounded continuously. How long will it take for his money to triple?

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Answer 1 · 2017-08-20T13:16:13

#approx 13.32# years

A principal amount of #$P#, compounded continuously at a rate of #r%#p.a. will grow to #$Q# after #t# years is given by:

#Q=Pe^(rt)#

In our example:

P=500, r=8.25%#, Q=3xx500 = 1500#

#:. 1500=500xxe^(8.25/100xxt)#

#e^(0.085t)=3#

#0.0825t = ln3#

#t = ln3/0.0825 approx 1.0986/0.0825#

#t approx 13.32# years

{NB: The principal is actually irrelevant here. Any amount will triple in #approx 13.32# years if compounded continuously at #8.25%# p.a.]