Question

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?

Answer 1

Answer:

Explanation:

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