To find the interest that Pam will earn in 3 years, we need to first calculate the total amount that she will have after 3 years by applying the interest. Since the interest is compounded quarterly and Pam is investing for 3 years, we can calculate the total amount that she will have after 3 years using the formula for the future value of an investment:
FV = P * (1 + i)^n
where FV is the future value, P is the initial investment, i is the interest rate per period, and n is the number of periods.
In this case, we know that P = $8,000, i = 4.8% / 4 = 1.2%, and n = 3 * 4 = 12, since the interest is compounded quarterly and Pam is investing for 3 years. Substituting these values into the formula above, we get:
FV = P * (1 + i)^n
FV = $8,000 * (1 + 0.012)^12
Calculating this value gives us FV = $8,976.73, which is the total amount that Pam will have after 3 years, including interest.
To find the amount of interest that Pam will earn in 3 years, we can subtract the initial investment from the total amount to get:
Interest = FV - P
Interest = $8,976.73 - $8,000
Interest = $976.73
Therefore, Pam will earn $976.73 in interest over 3 years.