Your client has a 12%, 20-year-mortgage on her home. The original amount of the

Question

Your client has a 12%, 20-year-mortgage on her home. The original amount of the loan was $175,000 when it was taken out exactly 7 years ago. Mortgage interest rates have fallen significantly, and your client thinks she could refinance the unpaid balance of the old loan at 8% for 13 years. She would have to pay two “points” as part of the refinancing costs, but these could be paid as part of the new loan, rather than in a lump sum. Based on this information, answer the following questions. (Your answer may differ slightly from those shown due to differences in rounding. What is the approximate unpaid balance on your client’s present mortgage?

A)$127,000

B) $151,900

C) $154, 600

D) $171, 200

E) $182, 600

Your client has a 12%, 20-year-mortgage on her home. The original amount of the loan was $175,000 when it was taken out exactly 7 years ago. Mortgage interest rates have fallen significantly, and your client thinks she could refinance the unpaid balance of the old loan at 8% for 13 years. She would have to pay two “points” as part of the refinancing costs, but these could be paid as part of the new loan, rather than in a lump sum. Based on this information, answer the following questions. (Your answer may differ slightly from those shown due to differences in rounding). What will be the approximate monthly payment for principal and interest if your client goes ahead with the refinancing?

A) $995

B) $1,412

C) $1,601

D) $1,656

E) $1,714

Explanation / Answer

To calculate the outstanding balance of original mortgage today, we first need to calculate the monthly payments on old mortgage. Note that there are 13x12 months=156 months remaining on the loan. The monthly interest rate is 12%/12=1%. The monthly payments can be calculated using below formula

Pmt = Lr / (1-(1+r)-t)

The amount you borrow is L, the interest rate per period is r, the number of periods is t, and P is the payment per period.

[($175,000 x 0.01) / (1-(1+0.01)-240)] = $1,926.90

Now, the outstanding balance can be computed using the present value formula,
PV = [($1,926.90/.01) x (1-(1/1.01156))]=$151,884

So, Option B (Approximately $151,900) is correct.

Now, to calculate the monthly payments, we first need to calculate the loan amount with refinancing cost as it will be paid as a part of new loan. Also for your information, one point equals to 1% of the loan amount in mortgages.

So, the new loan amount = $151,900 + (2% x $151,900) = $154,938

Now, we can calculate the monthly payments using the formula for monthly payment. The monthly interest rate will be 8%/12 = 0.6667%

[($154,938 x 0.0006667%) / (1-(1+0.06667%)-156)] = $1,600.62 or $1,601 approximately.

So, option C is correct.

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