An initial investment of $480 is appreciated for 8 years in an account that earns 9% interest, compounded quarterly. Find the amount of money in the account at the end of the period.
A $978.29
B $956.43
C $498.29
D $956.76
a = 480 [1 + (.09 / 4)]^(4 * 8)
To find the amount of money in the account at the end of the period, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount of money in the account
P = the initial investment
r = the annual interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the number of years the money is invested for
In this case, the initial investment is $480, the annual interest rate is 9% (or 0.09 as a decimal), the interest is compounded quarterly (n = 4), and the investment is for 8 years.
Plugging in these values into the formula, we get:
A = 480(1 + 0.09/4)^(4*8)
A = 480(1 + 0.0225)^(32)
A = 480(1.0225)^(32)
A ≈ $978.29
Therefore, the amount of money in the account at the end of the period is approximately $978.29.
So, the correct answer is option A: $978.29.