Answer:
$3,488.64
Explanation:
To calculate the amount after 5 years with an initial investment of $3,000 at a 3% interest rate compounded quarterly, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal (initial investment)
r = the annual interest rate (in decimal form)
n = the number of times the interest is compounded per year
t = the number of years
In this case, P = $3,000, r = 3% or 0.03 (since it's given in percentage), n = 4 (quarterly compounding), and t = 5 years.
Substituting the values into the formula:
A = 3000(1 + 0.03/4)^(4*5)
Simplifying the expression within the parentheses:
A = 3000(1 + 0.0075)^(20)
Calculating the value within the parentheses:
A = 3000(1.0075)^(20)
Using a calculator or performing the calculations:
A ≈ 3000 * 1.162881
A ≈ $3,488.64
Therefore, the amount after 5 years would be approximately $3,488.64.