Step 1 :Given: Principal amount (P) = $1024, annual interest rate (r) = 1.5% = 0.015 (in decimal), time (t) = 2 years, and number of times that interest is compounded per year (n) = 12.
Step 2 :We use the formula for compound interest: \(A = P(1 + r/n)^{nt}\)
Step 3 :Substitute the given values into the formula: \(A = 1024(1 + 0.015/12)^{12*2}\)
Step 4 :Calculate the value inside the parentheses: \(1 + 0.015/12 = 1.00125\)
Step 5 :Substitute this back into the formula: \(A = 1024(1.00125)^{24}\)
Step 6 :Calculate the exponent: \((1.00125)^{24} ≈ 1.030454897\)
Step 7 :Substitute this back into the formula: \(A = 1024 * 1.030454897 ≈ $1055.03\)
Step 8 :The interest earned is the final amount minus the principal: \(Interest = A - P = $1055.03 - $1024\)
Step 9 :\(\boxed{Interest = $31.03}\)