Question

The nominal monthly rate for a loan is quoted at 5%. What is the equivalent annual rate? Semiannual rate? Continuous rate?

Answer 1

ANSWER 1 :

NOMINAL RATE = 5% (MONTHLY COMPOUNDING)

SO EQUIVALENT ANNUAL RATE = (1 +0.05/12)¹² - 1 = 5.12%

ANSWER 1 : EQUIVALENT ANNUAL RATE = 5.12%

ANSWER 2 :

SEMI ANNUAL RATE = (1 + RATE/2)² = (1+0.05/12)¹² = 1.0512

(1 + RATE/2)² = 1.0512

TAKING SQUARE ROOT ---> (1 + RATE/2) = 1.02528

RATE = 5.056 %

ANSWER 2 : SEMI ANNUAL RATE = 5.056 %

ANSWER 3

CONTINUOUS RATE = e^r = (1+0.05/12)¹²

THEREFORE RATE =12* ln (1+0.05/12) = 12 * 0.004158 = 0.049896 = 4.99%

ANSWER 3 : CONTINUOUS RATE = 4.99%

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