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%

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