Clay deposited $500 in a savings account which pays 8.2% interest,

Question

compounded quarterly. What was his balance at the beginning of the
third quarter?

Answer 1

To calculate Clay's balance at the beginning of the third quarter, we need to determine the balance after the first two quarters of interest.

First, we need to calculate the interest earned after the first quarter:
Interest = Principal * (1 + (rate / n))^(n*t) - Principal
Interest = $500 * (1 + (0.082 / 4))^(4*1) - $500
Interest = $500 * (1 + 0.0205)^4 - $500
Interest = $500 * (1.0205)^4 - $500
Interest = $500 * 1.08344 - $500
Interest = $541.72 - $500
Interest = $41.72

After the first quarter, Clay's balance will be $500 + $41.72 = $541.72.

Next, we need to calculate the interest earned after the second quarter:
Interest = Principal * (1 + (rate / n))^(n*t) - Principal
Interest = $541.72 * (1 + (0.082 / 4))^(4*1) - $541.72
Interest = $541.72 * (1.0205)^4 - $541.72
Interest = $541.72 * 1.08344 - $541.72
Interest = $586.07 - $541.72
Interest = $44.35

After the second quarter, Clay's balance will be $541.72 + $44.35 = $586.07.

Therefore, Clay's balance at the beginning of the third quarter would be $586.07.