you deposit $2000 in an account that pays 2% annual
interest compounded quarterly.  How long will it 
take for the balance to reach $2400?

I have having trouble completing this problem, 
please help with the steps.

Tx, H




where

A = final amount
P = beginning amount
r = annual interest rate expressed as a decimal
n = number of times a year interest is compounded
t = number of years.

In this problem

A = $2400
P = $2000
r = .02
n = 4 (quarterly)
t = unknown

Substituting:







Divide both sides by 2000





take the natural log of both sides:



Use the rule of logarthims  on the
right hand side:



Divide both sides by 





Get your calculator and work out the left sides;



At the end of 9 years, the balance will be $2393.36
which is short of $2400 by $6.64, then on the next
compounding 3 months later, the balance will be 
$2408.34, which is over $2400 by $8.34.  The balance
won't ever reach $2400 exactly, but the first time 
it will exceed $2400 will be 9 years and 3 months.

Edwin