A. If the bank had compounded the interest quarterly for the three years, the interest rate would be divided by 4 (since there are 4 quarters in a year) and the number of compounding periods would be multiplied by 4. This is because the interest would be calculated and added to the account balance every quarter, rather than just once a year.
B. To represent the account balance if interest is compounded quarterly, we need to use the formula for compound interest with quarterly compounding:
A = P(1 + r/n)^(nt)
where A is the account balance, P is the principal (initial deposit), r is the annual interest rate (8.5%), n is the number of times the interest is compounded per year (4 for quarterly compounding), and t is the number of years (3).
Substituting the given values into the formula, we get:
A = 1500(1 + 0.085/4)^(4×3)
A = 1500(1.02125)^12
A ≈ $1,969.36
Therefore, the new expression for the account balance, in dollars, if interest is compounded quarterly is:
$1,969.36 = 1500(1 + 0.085/4)^(4×3)