# Converting interest rates

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.

## 1 Answer

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%). Sep 7, 2017 at 3:26
• @jiggunjer Indeed, or even w = (1 + a)^(7/365.2422) - 1 :-) Sep 7, 2017 at 12:15
• I already accounted for leap years by rounding to 30.4 :-) Sep 7, 2017 at 14:53