4% Monthly Compounded Rate to Semiannually Compounded Rate Conversion

Explanation

To solve such problems, think about investing a dollar for 1 year. The final amount should be the same under both the quotations. Under semiannually compounded rate, r, $1 grows to (1+r/2)^2 in 1 year. Under monthly compounding, it grows to (1+0.04/12)^12 = 1.0407. Since these two should be equal, we get

(1+r/2)^2 = 1.0407, giving r = 4.03%. Note that the semi-annually compounded rate must be larger than the monthly compounded rate, ruling out 3.96 automatically.