Question

The mortgage on your house is five years old. It required monthly payments of $1,402​, 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 6.125% ​(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 $1,402. How long will it take you to pay off the mortgage after​ refinancing? d. Suppose you are willing to continue making monthly payments of $1,402 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

First, we need to calculate the principal amount from the given data:

Monthly Payment = $ 1,402

Original Term = 30 years; n = 30 X 12 = 360 payment terms

Interest rate = 9% (APR) = 9% /12 = 0.75% per month

using the formula Mortgage Payments M = P X r X (1+r)^n / (((1+r)^n)-1)

Principal Amount = $ 1,74,243.18

Remaining principal amount as per the below table = $ 1,67,064.59

a. Monthly Payments required as per the new loan requirements = $ 1,015.10 as per the PMT function in excel PMT (6.125%/12, 360, $1,67,064.59,0)

b. Monthly Payments required as per the new loan requirements for payment to be made in 25 years = $ 1,089.20 as per the PMT function in excel PMT (6.125%/12, 300, $1,67,064.59,0)

c. Calculating Term (n) using goal seek in excel for the target payment of $ 1,402, number of years comes out to be 15.34 translating into 15 years and 5 months

d. With the existing payment of $ 1,402 to pay off mortgage in 25 years the principal amount using the M = P X r X (1+r)^n / (((1+r)^n)-1) comes out to be $ 2,15,042.56

The additional amount that can be borrowed comes out to be $ 2,15,042.56 - $ 1,67,064.59 = $ 47,977.97