Clay deposited $500 in a savings account which pays 8.2% interest,
compounded quarterly. What was his balance at the beginning of the
third quarter?
a. $520.71
b. $531.38
c. $510.25
d. $582.00
First, we need to determine how many quarters have elapsed before the beginning of the third quarter. There are 4 quarters in a year, so 2 quarters have elapsed (the beginning of the third quarter is the midpoint of the year).
To calculate the balance at the beginning of the third quarter, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = final amount
P = principal (initial deposit)
r = annual interest rate (8.2%)
n = number of times the interest is compounded per year (4 for quarterly)
t = time in years (2/4 = 0.5 for two quarters)
Plugging in the values, we get:
A = 500(1 + 0.082/4)^(4*0.5)
A = 531.38
Therefore, Clay's balance at the beginning of the third quarter was $531.38. The answer is (b).