SOLUTION: Jimmy invests ​$17,000 in an account that pays ​6.39% compounded quarterly. How long​ (in years and​ months) will it take for his investment to reach ​$​24,000?

Use the formula for the future value of a quarterly compounded account

    F =      (1)

where

F = future value,
A = present value (the starting deposit),
r = annual interest rate expressed as a decimal,
n = number of quarters.


For the amount of $17,000, compounded quarterly at 6.39% annual interest rate, the future value formula is

    F = 

where n is the number of quarters.



Therefore, our equation to find "n" is

    24000 = 


Divide both sides by 2100

     = ,

or

    1.411765 = .


Take logarithm base 10 of both sides

    log(1.411765) = n*log(1.015975)


and find the number of quarters "n" 

    n =  = 21.76  quarters.


Finally, round this decimal value 21.76 to the nearest greater integer number of quarters,
which is 22, in order for the bank was in position to make the last compounding.


ANSWER. 22 quarters, or 5 years and 6 months.