Converting interest rates

Question

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.

Answer 1

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.