SOLUTION: You deposit $800 in an account that pays 9% annual intrest compounded monthly. About how many years will it take for the account balance to reach $2400? Convert this to years and m

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: You deposit $800 in an account that pays 9% annual intrest compounded monthly. About how many years will it take for the account balance to reach $2400? Convert this to years and m      Log On


   

Question 183182: You deposit $800 in an account that pays 9% annual intrest compounded monthly. About how many years will it take for the account balance to reach $2400? Convert this to years and months.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
You deposit $800 in an account that pays 9% annual
interest compounded monthly. About how many years
will it take for the account balance to reach $2400?
Convert this to years and months.

A+=+P%281%2BR%2FN%29%5E%28NT%29

where A = Final Amount = $2400
      P = Beginning Amount = $800
      R = Rate expessed as a decimal = .09
      N = Number of compoundings per year = 12
      T = Number of years = ?  (What we must find)

We substitute for all but T

A+=+P%281%2BR%2FN%29%5E%28NT%29
2400+=+800%281%2B.09%2F12%29%5E%2812T%29
2400+=+800%281.0075%29%5E%2812T%29
2400%2F800+=+%28800%281.0075%29%5E%2812T%29%29%2F800
3+=+%281.0075%29%5E%2812T%29
ln%283%29=ln%281.0075%29%5E%2812T%29
ln%283%29=12T%2Aln%281.0075%29
ln%283%29%2F%2812ln%281.0075%29%29=T
ln%283%29%2F%2812ln%281.0075%29%29=T 
1.098612289%2F%2812%2A.0074720148%29=T

12.25252171=T

12 years

To get the months, multiply the decimal 
part .25252171 by 12

3.030260563 months

or about 12 years, 3 months.

Edwin