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Suppose the quoted APR is $r_0 = x-1$ and interest is compounded monthly;

Am I correct in saying the formula for the monthly interest rate $r$ is:

$$r = (1+ (\frac{r_0}{m}))^m -1 $$

Is it also correct to say that the present value of monthly repayments each of $A$ at an APR of $r0$ compounded monthly is:

$$PV = \frac{A}{(1+r_0/m)^{mt}} $$

And finally that the monthly payments on a mortgage of $P$ over $t$ years at an APR of $r0$ is:

$$R = \frac{P \cdot r0}{[1-(1+r_0)^{-m}]}$$

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The monthly interest rate is $\frac{r_0}{m}$ where $m=12$. The formula you give $$r = \left(1+ \frac{r_0}{m}\right)^m -1 $$ is the Effective Annual Rate corresponding to $r_0$ compounded monthly.

The second formula is correct.

In the third formula there seem to be several typographical errors involving "m" and "t" (which is missing).

$$R=\frac{(r_0/m)P}{1-(1+r_0/m)^{-mt}}$$

A good reference for these basic formulas is Wikipedia.

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