Respuesta :
The monthly payment for a mortgage is given as:
[tex]\begin{gathered} A=P\mleft\lbrace\frac{r(1+r)^{nt}}{(1+r)^{nt}-1}\mright\rbrace \\ \text{Where:} \\ A\colon Payment\text{ amount per month} \\ P\colon\text{Principal} \\ r\colon Monthly\text{ interest rate} \\ t\colon\text{Time(years)} \end{gathered}[/tex]Thus, we have:
[tex]\begin{gathered} 15000=P\mleft\lbrace\frac{\frac{9.8}{100\times12}(1+\frac{9.8}{100\times12})^{48}}{(1+\frac{9.8}{100\times12})^{48}-1}\mright\rbrace \\ 15000=P\mleft\lbrace\frac{0.008166(1+0.008166)^{48}}{(1+0.008166)^{48}-1}\mright\rbrace \\ 15000=P\mleft\lbrace\frac{0.008166(1.008166)^{48}}{(1.008166)^{48}-1}\mright\rbrace \\ 15000=P\mleft\lbrace\frac{0.008166(1.477536)}{1.477536-1}\mright\rbrace \\ 15000=P\mleft\lbrace\frac{0.012066}{0.477536}\mright\rbrace \\ 15000=0.02526P \\ P=\frac{15000}{0.02526} \\ P=593676.348 \end{gathered}[/tex]Thus, the total price of the lot is:
[tex]\begin{gathered} 450,000+593,676.348 \\ \Rightarrow1,043,676.34891 \end{gathered}[/tex]Hence, the correct option is option A
