Question

A leading bank is coming up with an investment that pays 8 percent interest compounded semiannually. What is the investment's effective annual rate (rEAR)?

Answer 1

The effective rate is calculated in the following way:

`r = {(1 + (i)/(n) )}^(n) - 1`
where r is the effective annual rate, i the interest rate, and n the number of compounding periods per year (for example, 12 for monthly compounding).
our compounding period is 2 since the bank pays us semiannually(two times per year) and our interest rate is 8%
so lets plug in numbers:

`r = {(1 + (8\%)/(2)) }^(2) - 1 \\ r = {(1 + (1)/(25)) }^(2) - 1 \\ r = (676)/(625) - 1 \\ r = 0.0816 \: or \: 8.16\%`