49.9k views
4 votes
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%

User Pavel Lint
by
8.7k points

1 Answer

3 votes

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%

User Peter Westlake
by
8.3k points