A 30-year fixed-rate mortgage has a contract rate of 7.00% with one point.A 15- year fixed-rate mortgage has a contract rate of 6.25%.If both loans have a 15-year holding period,what amount of points on the 15-year loan will equalize the effective costs of these loans over their holding periods? Assume a loan amount of
$80,000.

Question

Quizplus · Accepted Answer

To find the effective costs, we need to calculate the total interest paid over the 15-year holding period for each loan. For the 30-year loan, the total interest paid would be $81,181, and for the 15-year loan, the total interest paid would be $37,302.

To equalize the effective costs, we need to adjust the points on the 15-year loan. Let P be the points on the 15-year loan.

The total cost of the 30-year loan would be $161,202 ($80,000 loan amount + $81,181 interest + $800 one point).

The total cost of the 15-year loan would be $117,302 ($80,000 loan amount + $37,302 interest + $800 P points).

Setting these equal, we get:

$161,202 = $117,302 + $800P

Solving for P, we get P = 5.31 points.

A 30-Year Fixed-Rate Mortgage Has a Contract Rate of 7