Question

A bank offers 8.00% on savings accounts. What is the effective annual rate if interest is compounded semi-annually?Percentage Round to: 4 decimal places (Example: 9.2434%, % sign required. Will accept decimal format rounded to 6 decimal places (ex: 0.092434))

Answer 1

Answer:

Effective Annual Rate  = 8.1600%

Explanation:

The effective annual rate the interest rate that is adjusted for compounding over a given period of time. It is given by the formula:

$r = (1+\frac{i}{n})^n -1\\where:\\r = effective\ annual\ rate\\i = nominal\ interest\ rate\ = 8.00\% = 0.08 \\n = number\ of\ compounding\ periods\ per\ year\ = 2\ (semi-annually)$

$r = (1+\frac{0.08}{2})^2 -1\\r = (1\ +\ 0.04)^2 - 1\\r = (1.04)^2 - 1\\r = 1.0816 - 1\\r = 0.0816\\r = 8.1600 \%$