quartely payment A Loan of R65 000 with an interest rate of 16% per annum compounded quartely is to be amortised by equal quartely payments over 3 years
Question : how do I calculate the size of the quartely payment?
Will I = 0,016/4 and will n =36 months (3years)?
 A: For this question you can use the formula $A=P(1+\frac rn)^{nt}$. Where $P$ is your loan amount, $r$ is the rate, $n$ is the number of times compounded per year, and $t$ is the number of years.
In your case you would use $65000(1+\frac{.16}{4})^{4(3)}$.
I hope this helps.
A: $\displaystyle{%
 r \equiv 3\times\left(16/1200\right).\quad x_{0} \equiv 65,000.\quad
 n \equiv 12.\quad x \equiv \mbox{quarterly payment}\ =\, ?}$
\begin{align}
&\\[5mm]
x_{1} &= x_{0}\left(1 + r\right) - x
\\[1mm]
x_{2}
&=
x_{1}\left(1 + r\right) - x
=
x_{0}\left(1 + r\right)^{2} - x\left(1 + r\right) - x
\\[1mm]
x_{3}
&=
x_{2}\left(1 + r\right) - x
=
x_{0}\left(1 + r\right)^{3} - x\left(1 + r\right)^{2} - x\left(1 + r\right) - x
\\[1mm]\vdots &= \vdots
\\
x_{n}
&=
x_{0}\left(1 + r\right)^{n} - x\sum_{k = 0}^{n - 1}\left(1 + r\right)^{k}
=
x_{0}\left(1 + r\right)^{n} - x\,{\left(1 + r\right)^{n} - 1 \over r}
\end{align}
$x_{n} = 0\quad\Longrightarrow$
$$
\begin{array}{|c|}\hline\\
\color{#ff0000}{
{\large%
x
=
{r \over 1 - \left(1 + r\right)^{-n}}\ x_{0}}}
\\ \\\hline
\end{array}
$$
