Final answer:
Using the compound interest formula, A = P(1 + r/n)^(nt), the $500 deposited at a 3% interest rate for 10 years compounded annually would be worth approximately $579.64 after 5 years.
Step-by-step explanation:
If you deposited $500 in a bank with a 3% interest rate for 10 years, the calculation formula you would use to find out how much your account would be worth after 5 years with compounded interest is the compound interest formula:
A = P(1 + \frac{r}{n})^{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 time the money is invested for, in years.
Assuming the interest is compounded annually, the formula with the given values becomes:
A = 500(1 + \frac{0.03}{1})^{1*5}
A = 500(1 + 0.03)^5
A = 500(1.03)^5
A = 500 * 1.159274074
A ≈ $579.64
So, after 5 years, the account would be worth approximately $579.64.