SOLUTION: You deposit $300 each month into an account earning 8% interest compounded monthly. a) How much will you have in the account in 15 years? $ b) How much total money will

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Question 1150348: You deposit $300 each month into an account earning 8% interest compounded monthly.
a) How much will you have in the account in 15 years?
$

b) How much total money will you put into the account?
$

c) How much total interest will you earn?
$
Answer by ikleyn(52848) About Me  (Show Source):
You can put this solution on YOUR website!
.

It is a classic Ordinary Annuity saving plan. The general formula is 


    FV = P%2A%28%28%281%2Br%29%5En-1%29%2Fr%29,    (1)


where  FV is the future value of the account;  P is your monthly payment (deposit); r is the monthly percentage yield presented as a decimal; 
n is the number of deposits (= the number of years multiplied by 12, in this case).


Under the given conditions, P = 300;  r = 0.08/12;  n = 12*15 = 180.  So, according to the formula (1), you get at the end of the 15-th year


    FV = 300%2A%28%28%281%2B0.08%2F12%29%5E%2812%2A15%29-1%29%2F%28%280.08%2F12%29%29%29 = 300%2A%28%28%281%2B0.08%2F12%29%5E180-1%29%2F%28%280.08%2F12%29%29%29 = $103811.50.


Note that you deposit only  12*15*$300 = $54000.  

The rest, $103811.50 - $54000 = 49811.47 is what the interest.

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On Ordinary Annuity saving plans,  see the lessons
    - Ordinary Annuity saving plans and geometric progressions
    - Solved problems on Ordinary Annuity saving plans
in this site.

The lessons contain  EVERYTHING  you need to know about this subject,  in clear and compact form.

When you learn from these lessons,  you will be able to do similar calculations in semi-automatic mode.