Final answer:
To find the balance after 5 years with quarterly compounding, use the formula A = P(1 + r/n)^(nt), where A is the balance, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. Plug in the given values to calculate the balance as $7,242.60, which is approximately option a) $7,219.53.
Step-by-step explanation:
To find the balance after 5 years, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the balance, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, P = $6,000, r = 4% or 0.04, n = 4 (quarterly compounding), and t = 5.
Plugging in these values into the formula:
A = $6,000(1 + 0.04/4)^(4 * 5)
Simplifying the expression:
A = $6,000(1.01)^20
Calculating the exponent:
A ≈ $6,000(1.2071)
A ≈ $7,242.60
The balance after 5 years, when the interest is compounded quarterly, is approximately $7,242.60. Therefore, the correct answer is a) $7,219.53.