stephen has just purchased a home for $141,000. a mortgage company has approved his loan application for a…

Explanation:

Step1: Calculate the amount financed

The purchase - price of the home is $P = 141000$. The down - payment is 25% of the purchase price. So the amount financed $A=(1 - 0.25)\times141000=0.75\times141000 = 105750$.

Step2: Determine the number of periods for 20 - year and 30 - year mortgages

For a 20 - year mortgage, the number of months $n_1=20\times12 = 240$ months. For a 30 - year mortgage, the number of months $n_2=30\times12 = 360$ months. The annual interest rate $r = 4.75%=0.0475$, so the monthly interest rate $i=\frac{0.0475}{12}$. We use the formula for the monthly payment of a fixed - rate mortgage $M=\frac{A\times i\times(1 + i)^n}{(1 + i)^n-1}$. But we are given a table of monthly payment per $1000$ of the amount financed. The number of $1000$ units in the amount financed is $N=\frac{105750}{1000}=105.75$. Let $m_1$ be the monthly payment per $1000$ for a 20 - year mortgage and $m_2$ be the monthly payment per $1000$ for a 30 - year mortgage from the table. Suppose from the table, $m_1$ (monthly payment per $1000$ for 20 - year at 4.75%) and $m_2$ (monthly payment per $1000$ for 30 - year at 4.75%) are found. The monthly payment for a 20 - year mortgage $M_1 = 105.75\times m_1$. The monthly payment for a 30 - year mortgage $M_2 = 105.75\times m_2$. The increase in monthly payment $\Delta M=105.75\times(m_1 - m_2)$. Let's assume from the table that the monthly payment per $1000$ for a 20 - year mortgage at 4.75% is $m_1 = 6.61$ and for a 30 - year mortgage at 4.75% is $m_2 = 5.21$.

Step3: Calculate the increase in monthly payment

$\Delta M=105.75\times(6.61 - 5.21)$ $=105.75\times1.4$ $=148.05$

Answer:

$148.05$