SOLUTION: You deposit $400 each month into an account earning 2% interest compounded monthly. a) How much will you have in the account in 20 years? $ b) How much total money will

Algebra ->  Finance -> SOLUTION: You deposit $400 each month into an account earning 2% interest compounded monthly. a) How much will you have in the account in 20 years? $ b) How much total money will       Log On


   

Question 1122075: You deposit $400 each month into an account earning 2% interest compounded monthly.
a) How much will you have in the account in 20 years?
$

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

c) How much total interest will you earn?
$
Answer by ikleyn(52921) About Me  (Show Source):
You can put this solution on YOUR website!
.
There are two types of saving accounts that work in accordance with this scheme:

        a)  Ordinary Annuity saving plan,   and

        b)  Annuity Due saving plan.

Under Ordinary Annuity saving plan you deposit  $400  at the end of each month;
under Annuity Due saving plan you deposit  $400  at the beginning of each month.

I will give you the solution for the Ordinary Annuity plan only. 

     (When such a problem comes without explicit naming of the plan, I am 100% sure that it means an Ordinary Annuity).

The formula is 

    The future value in 20 years = 400%2A%28%28%281%2B0.02%2F12%29%5E%2820%2A12%29-1%29%2F%28%280.02%2F12%29%29%29%29 = 400%2A%28%28%281%2B0.02%2F12%29%5E240-1%29%2F%28%280.02%2F12%29%29%29%29 = $117918.73.


    Notice that you deposit only $400*12*20 = $96,000.

    The rest is compound percents that the account earns in 20 years.


a) How much will you have in the account in 20 years?

$  $117,918.73.


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

$  $96,000.


c) How much total interest will you earn?

%28%28117918.73+-+96000%29%2F96000%29%2A100 = 22.83%.

On both plans, you can learn and read from the lessons
    - Ordinary Annuity saving plans and geometric progressions
    - Annuity Due saving plans and geometric progressions
in this site.