SOLUTION: Solve the problem. The formula S = A((1+r)^t+1 -1 / r)models the value of a retirement account, where�A = the number of dollars added to the retirement account each year r= the

Question 1088342: Solve the problem.
The formula S = A((1+r)^t+1 -1 / r)models the value of a retirement account, where�A = the number of dollars added to the retirement account each year
r= the annual interest rate, and��s= the value of the retirement account after t years. If the interest rate is 11%, how much will the account be worth after 15 years if $1200 is added each year? Round to the nearest whole number.
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!
Question:
Solve the problem.
The following formula models the value of a retirement account,
S = A[(1+r)^(t+1)-1] / r)
where�
A = the number of dollars added to the retirement account each year
r= the annual interest rate, and��
s= the value of the retirement account after t years.
If the interest rate is 11%, how much will the account be worth after 15 years if $1200 is added each year? Round to the nearest whole number.

Solution:
[note question has been edited for readability and proper parentheses matching]
Important note:
The formula contains the term t+1 instead of the usual "t". This means that the formula applies only in the case where the money is invested at the beginning of the year (period) instead of the usual practice at the end.
We're given
A=1200
r=0.11
t=15
Accumulated amount,
F=A((1+r)^(t+1)-1)/r
=1200(1.11^(15+1)-1)/0.11
=47027.94 [to two decimals, round to dollar as required]

If money is invested at the end of the year (usual practice), then
F=$41286.43, the difference being the investment of an extra 1200 over 15 years.

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