# Interest rates compounded monthly [closed]

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:

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

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.