You choose to invest your $3,560 income tax refund check (rather than spend it!) in an account earning 5% compounded semiannually. How much will the account be worth in 5 years?

P = Po(1+r)^n.

Po = $3500.

r = 0.05/2 = 0.025.

n = 2Comp./yr. * 5yrs. = 10 Compounding periods.

P = ?.

To find the amount your account will be worth in 5 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = Total amount after interest
P = Principal amount (initial investment)
r = Annual interest rate (in decimal)
n = Number of times interest is compounded per year
t = Number of years

In this case, your principal amount is $3,560, the annual interest rate is 5% (or 0.05 in decimal form), interest is compounded semiannually (n = 2), and the investment duration is 5 years (t = 5).

Plugging the values into the formula:

A = 3,560 * (1 + 0.05/2)^(2*5)

Let's solve it step by step.

First, calculate the exponent part:
(1 + 0.05/2)^(2*5) = (1.025)^10 ≈ 1.28008403

Now, substitute it back to the formula:
A = 3,560 * 1.28008403

Finally, calculate the answer:
A ≈ $4,556.61

Therefore, your account will be worth approximately $4,556.61 after 5 years if the interest is compounded semiannually at a 5% annual interest rate.