Mr chua borrows a sum of from the bank which charges a compound interest of 4.2% per annum, compounded quarterly. Given that Mr chua had to pay $96.60 in interest payments at the end of the first year, find the original sum of money borrowed, giving your answer correct to the nearest cent.
+118609 Interest = FV- PV
$$\\FV=PV*(1+0.042/4)^4\\\\
I=PV*(1+0.042/4)^4-PV\\\\
96.60=PV((1+0.042/4)^4-1)\\\\
PV=96.60\div ((1+0.042/4)^4-1)$$
$${\frac{{\mathtt{96.6}}}{\left({\left({\mathtt{1}}{\mathtt{\,\small\textbf+\,}}\left({\frac{{\mathtt{0.042}}}{{\mathtt{4}}}}\right)\right)}^{{\mathtt{4}}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}} = {\mathtt{2\,264.090\: \!306\: \!474\: \!847\: \!048\: \!9}}$$
Amount borrowed $2264.09
+118609 Interest = FV- PV
$$\\FV=PV*(1+0.042/4)^4\\\\
I=PV*(1+0.042/4)^4-PV\\\\
96.60=PV((1+0.042/4)^4-1)\\\\
PV=96.60\div ((1+0.042/4)^4-1)$$
$${\frac{{\mathtt{96.6}}}{\left({\left({\mathtt{1}}{\mathtt{\,\small\textbf+\,}}\left({\frac{{\mathtt{0.042}}}{{\mathtt{4}}}}\right)\right)}^{{\mathtt{4}}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}} = {\mathtt{2\,264.090\: \!306\: \!474\: \!847\: \!048\: \!9}}$$
Amount borrowed $2264.09
