Equivalent Annually Compounded Rate Calculation

A

To solve such problems, think about investing a dollar for a year. The final amount should be the same under both the quotations. Under annually compounded rate, r, $1 grows to 1+r in 1 year. Under semiannual compounding, it grows to (1+0.1/2)^2 = 1.1025. Since these two should be equal, we get 1+r = 1.1025, giving r = 10.25%. Note that the annually compounded rate must be larger than the semiannually rate, ruling out 9.65 automatically.