Final answer:
The accumulated value of an investment of $100 at 12% compounded quarterly for 4 years is $162.69.
Step-by-step explanation:
The formula to calculate the accumulated value of an investment with compound interest is:
A = P(1 + r/n)^(nt)
Where:
A: Accumulated value
P: Principal amount
r: Interest rate
n: Number of times the interest is compounded per year
t: Number of years
In this case, we have:
P = $100
r = 12% = 0.12
n = 4 (compounded quarterly)
t = 4 years
Plugging the values into the formula, we get:
A = 100(1 + 0.12/4)^(4*4) = $100(1.03)^16 = $100(1.626897) = $162.69
Therefore, the accumulated value of the investment after 4 years is $162.69.