2

I have found a monthly interest rate, 0.72%

Now, I would like to convert this monthly rate to:

  1. Equivalent annual nominal rate of interest payable half yearly, and
  2. Equivalent annual nominal rate of interest payable weekly

    For 1. I used (i12 + 1)^6 - 1 so (0.72+1)^(6)-1 = 4.41%
    and 2. I used (i12 + 1)^0.230137 = (0.72+1)^(0.230137)-1 = 0.17%



Is this the correct approach?


Thanks for any assistance.

5

If m is the monthly rate 0.72%

m = 0.72/100

Find the annual effective rate a = (1 + m)^12 - 1 = 0.0899049 so 9%

The half-yearly rate h = (1 + a)^(1/2) - 1 = 0.0439851

so the nominal APR compounded half-yearly is 2 h = 0.0879702 so 8.797%

The weekly rate w = (1 + a)^(1/52) - 1 = 0.00165696

so the nominal APR compounded week is 52 w = 0.0861617 so 8.616%

Check

The half-yearly, monthly & weekly rates produce the same result when compounded over one year.

(1 + h)^2  - 1 = 8.99049%
(1 + m)^12 - 1 = 8.99049%
(1 + w)^52 - 1 = 8.99049%

For more info see the Effective Interest Rate Calculation.

  • If you assume the monthly rate is based on 30.4 days average, then the weekly rate might be better calculated by: w = (1 + a)^(7/365) - 1. This would give a slightly lower rate (8.59%). – jiggunjer Sep 7 '17 at 3:26
  • @jiggunjer Indeed, or even w = (1 + a)^(7/365.2422) - 1 :-) – Chris Degnen Sep 7 '17 at 12:15
  • I already accounted for leap years by rounding to 30.4 :-) – jiggunjer Sep 7 '17 at 14:53

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