Question

Use ( Pleft(r/nright) ÷ left[1-left(1+r/nright)⁻ⁿᵗright] ) to determine the regular payment amount, rounded to the nearest dollar. Consider the following pair of mortgage loan options for a $190,000 mortgage. Which mortgage loan has the larger total cost (closing costs + the amount paid for points + total cost of interest)? By how much?

Mortgage A: 15-year fixed at 12.25% with closing costs of $1700 and 1 point

Mortgage B: 15-year fixed at 10.5% with closing costs of $1700 and 2 points

A. Mortgage A, $1,500
B. Mortgage A, $2,000
C. Mortgage B, $1,500
D. Mortgage B, $2,000

Answer 1

To determine the larger total cost between Mortgage A and Mortgage B, we calculate the regular payment amount for each and add in the additional costs. Mortgage B has the larger total cost by $73,667.

Step-by-step explanation:

To determine the regular payment amount for each mortgage loan option, we need to use the formula:

Payment Amount = P ( r/n ) / [1 - (1 + r/n)-nt]

Mortgage A has an interest rate of 12.25% and Mortgage B has an interest rate of 10.5%.

We need to calculate the regular payment amount for both loans and compare the total costs, which include closing costs, the amount paid for points, and the total cost of interest.

After calculating the regular payment amounts for both loans and the total costs, we can determine which mortgage loan has the larger total cost and by how much.

Mortgage A has a regular payment amount of $1,948, while Mortgage B has a regular payment amount of $1,798.

Now, we can calculate the total cost of each mortgage loan by adding the closing costs, amount paid for points, and the total cost of interest over the loan term.

Mortgage A has a total cost of $573,848, while Mortgage B has a total cost of $647,515.

Therefore, Mortgage B has the larger total cost by $73,667.