To find the equivalent interest rate and the number of times the money will be compounded, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the amount of money at the end of the investment period, P is the initial investment, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the investment period in years.
In this case, P = $500, r = 8%, n = 52 (since the interest is compounded weekly), and t = 12 years. We can plug these values into the formula and solve for A:
A = $500(1 + 0.08/52)^(52*12) ≈ $1,333.30
So after 12 years, the investment will be worth approximately $1,333.30.
To find the equivalent interest rate, we can use the formula:
(1 + i) = (1 + r/n)^n
where i is the equivalent interest rate. Plugging in the values, we get:
(1 + i) = (1 + 0.08/52)^52
(1 + i) ≈ 1.0838
i ≈ 0.0838 or 8.38%
So the equivalent interest rate is approximately 8.38% and the money will be compounded 52 times per year (weekly).