Compound Interest

Date: 04/11/97 at 19:47:10
From: charles
Subject: Compound Interest

How many years (to the nearest tenth) will be needed for $5000 to 
increase to $22,000 at 11 percent interest compounded monthly?

Date: 04/13/97 at 08:00:33
From: Doctor Anthony
Subject: Re: Compound Interest

The monthly interest rate is 11/12 = 0.91666.

Use the formula   

   A = P(1 + r/100)^n

where A = amount = 22,000, P = principal = 5000, 
r = interest rate/month = 0.91666, and n = number of months.

   22000 = 5000(1.0091666)^n.

So 1.009166^n = 22/5 = 4.4    Now take the natural logs, so

   n*ln(1.0091666) = ln(4.4)
   n = ln(4.4)/ln(1.0091666)
     = 162.37 months
     = 13.53 years
     = 13 years 6 months.

-Doctor Anthony,  The Math Forum
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