In general, the compound interest formula is
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ P\to\text{initial amount} \\ r\to\text{ interest rate} \\ n\to\text{ number of times interest applied per time period} \\ t\to\text{ time (in time periods)} \end{gathered}[/tex]
Therefore, in our case,
[tex]n=12,t=2,A=45000,r=60\%=0.6[/tex]
Thus,
[tex]\begin{gathered} \Rightarrow45000=P(1+\frac{0.6}{12})^{12\cdot2} \\ \Rightarrow P=\frac{45000}{(1+\frac{0.6}{12})^{12\cdot2}} \\ \Rightarrow P=\frac{45000}{(1.05)^{24}} \end{gathered}[/tex]
a) Thus, the exact amount is 45000/(1.05)^24 dollars.
b) Rounding to two decimal places,
[tex]\begin{gathered} \Rightarrow P=13953.05596\ldots \\ \Rightarrow P=13953.06 \end{gathered}[/tex]
The rounded answer is $13953.06
