Deon has $4000.00 invested at 4.5% compounded semi-annually at her bank. In order to make a comparison with another financial institution she needs to know the effective rate of interest at her bank. What is the effective annual rate of interest?
A) 1.12%
B) 2.28%
C) 9.10%
D) 4.55%
E) 4.5%

Question

Quizplus · Accepted Answer

The effective annual rate (EAR) can be calculated using the formula for compound interest: EAR = (1 + i/n)^(n*t) - 1, where i is the annual interest rate, n is the number of compounding periods per year, and t is the time in years. For Deon's investment, i = 4.5% or 0.045, n = 2 (since it's compounded semi-annually), and t = 1 year. Plugging these values into the formula gives EAR = (1 + 0.045/2)^(2*1) - 1 = 1.0225^2 - 1 = 1.0455625 - 1 = 0.0455625 or 4.55%.

Deon Has $4000