The mortgage on your house is five years old. It required monthly payments of $1,450 , had an original term of 30 years, and had an interest rate of 9% (APR). In the intervening five years, interest rates have fallen and so you have decided to refinancelong dash that is, you will roll over the outstanding balance into a new mortgage. The new mortgage has a 30-year term, requires monthly payments, and has an interest rate of 6.625% (APR).

a. What monthly repayments will be required with the new loan?

b. If you still want to pay off the mortgage in 25 years, what monthly payment should you make after you refinance?

c. Suppose you are willing to continue making monthly payments of $1,450. How long will it take you to pay off the mortgage after refinancing?

d. Suppose you are willing to continue making monthly payments of $1,450 and want to pay off the mortgage in 25 years. How much additional cash can you borrow today as part of the refinancing?

Question

Jerimiah Mora

Business

18 June, 22:31

The mortgage on your house is five years old. It required monthly payments of $1,450 , had an original term of 30 years, and had an interest rate of 9% (APR). In the intervening five years, interest rates have fallen and so you have decided to refinancelong dash that is, you will roll over the outstanding balance into a new mortgage. The new mortgage has a 30-year term, requires monthly payments, and has an interest rate of 6.625% (APR).

a. What monthly repayments will be required with the new loan?

b. If you still want to pay off the mortgage in 25 years, what monthly payment should you make after you refinance?

c. Suppose you are willing to continue making monthly payments of $1,450. How long will it take you to pay off the mortgage after refinancing?

d. Suppose you are willing to continue making monthly payments of $1,450 and want to pay off the mortgage in 25 years. How much additional cash can you borrow today as part of the refinancing?

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Answers (1)

Know the Answer?

Ben Roach · Answer 1

Payments (P) = 1450

n = 30years; 30*12 months

APR (c) = 9%; 0.09/12 monthly = 0.0075

L - loan

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

1450 = L[0.0075 (1+0.0075) ^360]/[ (1+0.0075) ^360 - 1]

L = 180208.7

Balance loan

B = L[ (1 + c) ^n - (1 + c) p]/[ (1 + c) ^n - 1]

= 180208.7[ (1+0.0075) ^360 - (1+0.0075) 1450]/[ (1+0.0075) ^360 - 1]

= 172784.35

a. Monthly payments required on the new loan

APR = 6.625%; 0.00552 monthly

=172784.35 * [0.00552 * (1+0.00552) ^360]/[ (1+0.00552) ^360 - 1] = 1106.36

b. n = 25years; 300 months

P = 172784.35 * [0.00552 (1+0.00552) ^300]/[ (1+0.00552) 300 - 1] = 1180.18

c.

1450 = 172784.35[0.0075 (1+0.0075) ^ (n*12) ]/[ (1+0.0075) ^ (n*12) - 1]

n = 16.23 years

d.

1450 = L[0.0075 (1+0.0075) ^300]/[ (1+0.0075) ^300 - 1]

L = 212286.65

Additional cash = 212286.65 - 172784.35 = 39502.3