Question

The Rabiha Family decided to get a lot. They paif 450,000 for the down payment. The remaining account will be settled if they pay 15,000 at the end of each month for 4 years with the interest of 9.8% compounded monthly. What is the total price of the lot?*1,043,668*593,668*593,663*1,043,663

Answer 1

The monthly payment for a mortgage is given as:

`\begin{gathered} A=P\mleft\lbrace(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}`

Thus, we have:

`\begin{gathered} 15000=P\mleft\lbrace((9.8)/(100*12)(1+(9.8)/(100*12))^(48))/((1+(9.8)/(100*12))^(48)-1)\mright\rbrace \\ 15000=P\mleft\lbrace(0.008166(1+0.008166)^(48))/((1+0.008166)^(48)-1)\mright\rbrace \\ 15000=P\mleft\lbrace(0.008166(1.008166)^(48))/((1.008166)^(48)-1)\mright\rbrace \\ 15000=P\mleft\lbrace(0.008166(1.477536))/(1.477536-1)\mright\rbrace \\ 15000=P\mleft\lbrace(0.012066)/(0.477536)\mright\rbrace \\ 15000=0.02526P \\ P=(15000)/(0.02526) \\ P=593676.348 \end{gathered}`

Thus, the total price of the lot is:

`\begin{gathered} 450,000+593,676.348 \\ \Rightarrow1,043,676.34891 \end{gathered}`

Hence, the correct option is option A