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Solving for Time and Rates

Let's do another one:

How long will it take $10,000 to grow to $200,000 if it is invested at 7.5% compounded continuously?

* Compounded continuously means that we need to use this guy:

A = Pe^( rt )

200,000 = 10,000e^( .075t ) ... 20 = e^( .075t ) ... kill the e! ... Ln( 20 ) = Ln( e^( .075t ) ) ... Ln( 20 ) = .075t ... Ln( 20 ) / .075 = t ... t = approximately 39.9 years

It will take about 39.9 years for $10,000 to grow into $200,000 if it is invested at 7.5% compounded continuously.

 

TRY IT:

How long will it take $2000 to grow into $6000 if it is invested at 10% compounded monthly?

How long will it take $5039 to grow into $20,000 if it is invested at 4.6% compounded continuously?

If an alien amoeba splits into 1.7 alien amoebas every day, how long will it take for 1000 alien amoebas to grow into 42,000 alien amoebas?