Expert: Steve Holleran - 3/6/2007

Question
I usually understand math but this problem, I just don't comprehend.

Genreal:Intresr A bank offers 6 compounded continuously. How soon will a deposit.
a. quadruple?
b. increase by 75%

If you can help me figure this problem i would greatly appericiate it.
Thanks, Alicia  

Answer
Hi Alicia,

Hey, no need to panic here, this will work out fine.

What we need to note is the formula for continuous compounding.  If we let A = the amount of $ we want,
P = the Principal amount invested, r = interest rate as a decimal, and t = time in years, the formula is

             A = P * e^(rt)   where e is the exponential
                              number (2.71828....)

(I'm assuming you have a scientific or graphing calculator with an e^x  or ln x key.  You'll need this to do the calculating).

For the first one, we want A to = 4P ($ to quadruple)
So we have:

           4P = P * e ^(.06t)  and the P's divide out :

            4 = e^(.06t)  Now change this to a logarithm
                                       equation:

          .06t = ln 4   and t = ln 4 / .06  = 23.1

So, at 6% continuous, it will take 23.1 yrs for your money to quadruple in value.

For the second part, its the same except we want A = 1.75P:

                1.75 P  = P * e^(.06t)

Again, the P's divide out, and we get

                 1.75 = e^(.06t)

and so              .06t = ln 1.75  

and                     t = ln 1.75 / .06 = 9.3

So, it only takes 9.3 yrs to increase your principal by 75%

I hope this was clear, and helps you out.