Question Help the amount paid for points Consider the following pair of mortgage

Question

Question Help the amount paid for points Consider the following pair of mortgage loan options for a $165,000 mortgage. Which mortgage loan has the larger total cost (closing costs total cost of interest)? By how much? Mortgage A: 15-year fixed at 12.25% with closing costs of $1400 and 1 point. Mortgage B: 15-year fixed at 11.25% with closing costs of $1400 and 3 points. Choose the correct answer below, and fill in the answer box to complete your choice. OA. Mortgage B has a larger total cost than mortgage Aby $ OR, Mortgage Ahas a larger total cost than mortgage B by Round to the nearest dollar as needed)

Explanation / Answer

We know that 1 mortgage point costs 1 % of the mortgage amount ( paid to the lender at the time of closing) and has the effect of reducing the rate of interest by 0.25 %.

Mortgage A: It is a 15-year mortgage with effective interest rate of 12 % and a closing cost of $ (1400+ 1650) = $ 3050.

Mortgage B: It is a 15-year mortgage with effective interest rate of 10.50 % and a closing cost of $ (1400+ 3*1650) = $ 6350.

The fixed monthly payment in case of mortgage A is 165000*(12/1200)[(1+12/1200)15*12]/ [(1+12/1200)15*12 -1] = 1650(5.995801975)/4.995801975 = $ 1980.28 (on rounding off to the nearest cent). Thus, the total cost of the mortgage A is $ 1980.28 * 180 + 3050 = $ 359500.40.

The fixed monthly payment in case of mortgage B is 165000*(10.5/1200)[(1+10.5/1200)15*12]/ [(1+10.5/1200)15*12 -1] = (1443.75)*4.797760797/3.797760797 = $ 1823.91(on rounding off to the nearest cent). Thus, the total cost of the mortgage B is $ 1823.91 * 180 +6350 = $ 334653.80.

Thus, mortgage A has a larger total cost than mortgage B by $359500.40-$334653.80 = $ 24846.60

Note:

The formula used to calculate the fixed monthly payment (P) required to fully amortize a loan of $ L over a term of n months at a monthly interest rate of r is

P = L[r(1 + r)n]/[(1 +r)n - 1]

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.