Question

If $240 is invested at an interest rate of 9% per year and is compounded monthly, how much will the investment be worth in 14 years? (1 point)

Answer 1

Since the annual rate is 9% and we wish to know what it is worth after 14 years, that it compounds monthly is irrelevant.

f=240(1.09)^t, when t=14 you have:

f=240(1.09)^14

f=$802.01  (to nearest cent)

...

We COULD have taken into account monthly compounding...

1.09=r^12

r=1.09^(1/12)

then

f=240(1.09)^(1/12)^t  in this case t is in months so if we want it in years... it will be 12t then this becomes what we had before:

f=240(1.09)^(12t/12)

f=240(1.09)^t

f=240(1.09)^(t/12), if we allowed t to be in months not years, so t=14*12=168

f=240(1.09)^(168/12) which again makes the value the same:

f=240(1.09)^14  notice that the exponent becomes years again :P

I just show all of this so that you know when compounding occurs does not matter for these types of problems, even for continuous compounding problems.  The only time that it DOES matter is in accounts where additional deposits are made to the initial principle.  THEN when compounding occurs makes a significant difference.