+118724 I am assuming this is the question
$6000 borrowed and paid back monthly over 4 years.
The interest rate is 9.5% per annum compounded monthly.
Find monthly repayment.
This is a present value of an ordinary annuity problem.
A=6000
n=4*12=48
i=0.095/12 = 0.007916666666...
$$\begin{array}{rll}
A&=&R\times \frac{1-(1+i)^{-n}}{i}\\\\
6000&=&R\times \frac{1-(1.007916666666)^{-48}}{0.007916666666}\\\\
6000\div \left(\frac{1-(1.007916666666)^{-48}}{0.007916666666}\right)&=&R \\\\
\end{array}$$
$${\frac{{\mathtt{6\,000}}}{\left({\frac{\left({\mathtt{1}}{\mathtt{\,-\,}}{\left({\mathtt{1.007\: \!916\: \!666\: \!666\: \!666\: \!6}}\right)}^{-{\mathtt{48}}}\right)}{{\mathtt{0.007\: \!916\: \!666\: \!666\: \!66}}}}\right)}} = {\mathtt{150.738\: \!820\: \!025\: \!488\: \!329\: \!5}}$$
So, unless I made a stupid mistake the repayments will be $150.74 per month.
+118724 I am assuming this is the question
$6000 borrowed and paid back monthly over 4 years.
The interest rate is 9.5% per annum compounded monthly.
Find monthly repayment.
This is a present value of an ordinary annuity problem.
A=6000
n=4*12=48
i=0.095/12 = 0.007916666666...
$$\begin{array}{rll}
A&=&R\times \frac{1-(1+i)^{-n}}{i}\\\\
6000&=&R\times \frac{1-(1.007916666666)^{-48}}{0.007916666666}\\\\
6000\div \left(\frac{1-(1.007916666666)^{-48}}{0.007916666666}\right)&=&R \\\\
\end{array}$$
$${\frac{{\mathtt{6\,000}}}{\left({\frac{\left({\mathtt{1}}{\mathtt{\,-\,}}{\left({\mathtt{1.007\: \!916\: \!666\: \!666\: \!666\: \!6}}\right)}^{-{\mathtt{48}}}\right)}{{\mathtt{0.007\: \!916\: \!666\: \!666\: \!66}}}}\right)}} = {\mathtt{150.738\: \!820\: \!025\: \!488\: \!329\: \!5}}$$
So, unless I made a stupid mistake the repayments will be $150.74 per month.
