An interest rate is 5% per annum with continuous compounding. what is the equivalent rate with semiannual compounding?

a. 5.06%

b. 5.03%

c. 4.97%

d. 4.94%

The effective rate with continuous compounding is

... R = (e^r) - 1

... R = e^.05 - 1 ≈ 5.1271%

The effective rate with semiannual compounding is

... R = (1 + r/2) ² - 1

We want these to be the same, so we want ...

... 0.051271 = (1 + r/2) ² - 1

... √1.051271 = 1 + r/2

... r = 2 (√1.051271 - 1) ≈ 5.063%

The best choice is ...

... a. 5.06%