For the amount of 5000 pesos, compounded quarterly at 6.5% per year, the future value formula is

    Future Value = 

where n is the number of quarters.



Therefore, our equation to find "n" is


    7700 = 


Divide both sides by 5000


     = ,

or

    1.54 = .


Take logarithm base 10 of both sides


    log(1.54) = n*log(1.01625)


and find "n" using your calculator


    n =  = 26.77  quarters.


Finally, round this value 26.77 to the nearest greater integer 27,

in order for the bank was in position to make the last compounding.


ANSWER. 27 quarters, or 6 years and 9 months; 

        or, if you wat to round to the nearest year, 7 years.