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

To calculate the balance in Cathy's account after a certain number of years, we can use the given formula:

B = A(1 + r)^n + 1 - A

Where:
- B is the balance in her account
- A is the amount invested per year (which is $1,200 in this case)
- r is the interest rate (6.3% in this case)
- n is the number of years of investing

Let's use an example to understand how to use this formula. Let's say Cathy wants to know the balance in her account after 5 years.

1. Plug in the values:
A = $1,200
r = 6.3% (convert to decimal by dividing by 100: 0.063)
n = 5

2. Substitute the values into the formula:
B = $1,200(1 + 0.063)^5 + 1 - $1,200

3. Simplify the equation:
B = $1,200(1.063)^5 + 1 - $1,200

4. Calculate the exponent:
B = $1,200(1.383018802) + 1 - $1,200

5. Multiply and subtract:
B = $1,659.62 + 1 - $1,200

6. Simplify:
B = $1,660.62 - $1,200

7. Calculate the final balance:
B = $460.62

So, after 5 years of investing $1,200 per year at an interest rate of 6.3%, the balance in Cathy's account would be $460.62.

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".