A mortgage effective $\frac{1}{1}\frac{?}{2016}$ is being amortized by equal monthly installments of $x$

over five years including interest at a nominal annual rate of $12\%$ compounded monthly.

The first installment was due $\frac{2}{1}\frac{?}{2016}$ and the last installment was to be due $\frac{1}{1}\frac{?}{2021}.$

Immediately after the $24$th installment was made on $\frac{1}{1}\frac{?}{2018},$ a new level monthly

installment $Y$ is determined $($using the same rate of interest$)$ to shorten the total

amortization period to $3\mathrm{.}5$ years so that the final installment will fall due on $\frac{7}{1}\frac{?}{2019}.$

In which of the following ranges is the ratio Y$/$X$?$

Possible Answers

$<mn\; id="EditorElement\_1429556">1</mn><mn\; id="EditorElement\_1429557">.</mn><mn\; id="EditorElement\_1429558">2</mn><mn\; id="EditorElement\_1429559">5</mn>$

$1\mathrm{.}25$ but $<mn\; id="EditorElement\_1429580">1</mn><mn\; id="EditorElement\_1429581">.</mn><mn\; id="EditorElement\_1429582">5</mn><mn\; id="EditorElement\_1429583">0</mn>$

$1\mathrm{.}50$ but $<mn\; id="EditorElement\_1429604">1</mn><mn\; id="EditorElement\_1429605">.</mn><mn\; id="EditorElement\_1429606">7</mn><mn\; id="EditorElement\_1429607">5</mn>$

$1\mathrm{.}75$ but $<mn\; id="EditorElement\_1429628">2</mn><mn\; id="EditorElement\_1429629">.</mn><mn\; id="EditorElement\_1429630">0</mn><mn\; id="EditorElement\_1429631">0</mn>$

$2\mathrm{.}00$