Chapter 8.5, Problem 57E

Total cost of a mortgage. Legends often require home buyers to pay “points.” A point is $1\%$ of the purchase price of the home. In addition, the buyer also pays closing costs at the time of purchase. If you are taking out a 30-year mortgage for $\$140,000$, calculate the total costs for option A and option B below, that is,

$\text{Total cost}=& \text{points}+\text{closing costs}+\text{total mortgage payments}$.

Which option, A or B, has the greater total cost? Assume that points and closing costs are paid separately and are not included in the mortgage.

Use Table 8.6 for monthly payments.

A: Annual interest rate $5\%$; 2 points; closing costs $\$4,500$.

B: Annual interest rate $6\%$; 1 points; closing costs $\$2,500$.