Alliance Industries sets aside ​$4900.00 at the beginning of every six months in a fund to replace equipment. If interest is 4% compounded annually, how much will be in the fund after 10 ​years?
The fund will be worth $__________________



Answer :

To find out how much will be in the fund after 10 years with annual compounding interest of 4%, we need to use the formula for compound interest:

\[ A = P \left(1 + \frac{r}{n} \right)^{nt} \]

where:

- \( A \) is the amount of money accumulated after n years, including interest.

- \( P \) is the principal amount (the initial amount of money).

- \( r \) is the annual interest rate (decimal).

- \( n \) is the number of times that interest is compounded per year.

- \( t \) is the number of years the money is invested for.

Given:

- \( P = 4900.00 \) (amount set aside at the beginning of every six months, so we consider this as the principal for each period)

- \( r = 0.04 \) (4% annual interest rate, compounded annually)

- \( n = 1 \) (compounded annually)

- \( t = 10 \) years (total duration)

### Step-by-Step Calculation:

1. **Calculate the semi-annual contribution period:**

  The annual rate