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.