Question

Each year, Cathy invests $1,200 in
her account. The account pays an
interest rate of 6.3%. The formula to
calculate the balance in her account
is B =A(1+ r)n+1- A, where
r
A is the amount invested per year,
r is the interest rate, and n is the
number of years investing

Answer 1

Not sure what your question is, but the formula does not look right. You may want to check the post for typos.

If someone invests $A at the beginning of the year, at the end of one year, the balance is $A plus the interest, which is $Ar. So the balance is A(1+r).
For two years, it would be the sum of two investments,
A(1+r)²+A(1+r)
for n years, it would then be:
A[(1+r)+(1+r)²+(1+r)³...+(1+r)^n]
which is algebraically equal to
A[(1+r)^(n+1)-1)]/r - A
=A[((1+r)^(n+1)-1)/r - 1]
slightly different from yours. Your formula seems to miss out the "/r".