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### 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
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Interest

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