SOLUTION: Linda invests $12,000 earned by winning a singing contest in a certificate of deposit paying 1.5% interest compounded monthly. What are the total amount and the interest? could

The 1.5% annual interest compounded monthly is nominal (i.e., NOT factual).


The factual multiplicative rate of growth is    per month.


It means, that at the end of every month the amount at the account increases with the factor .


So, the original amount of 12000 dollars will be    dollars at the end of the 1-st month;

                                         will be    dollars at the end of the 2-nd month;

                                         will be    dollars at the end of the 3-rd month;


     . . . . . . .   and  so  on  . . . . . 


                                         will be    dollars at the end of the 12-nd month, 
                                         i.e. after 1 year.


So, after 1 years (12 compounding periods) the amount will be  

    Future Value =  = 12181.24  dollars.


The factual annual interest is then   = 0.015103 = 1.5103%.


The formula for the future value works for any given number of compounding periods, too

    Future Value =  ,


where "n" is the number of months.

    What are the total amount and the interest in 1 year ?   in 2 years ?  in 5 years ?    or in 18 months,  and so on . . .