Paying Off That Dream House When Jacqueline and Keith Sommers were \"house hunti

Question

Paying Off That Dream House When Jacqueline and Keith Sommers were "house hunting" five years ago, the mortgage rates were pretty high. The fixed rate on a 30-year mort- gage was 7.25%, while the 15-year fixed rate was at 6.25%. After walking through many homes, they finally reached a consensus and decided to buy a $300,000, two-story house in an up-and-coming suburban neighborhood in the Midwest. To avoid prepaid mortgage insurance (PMI), the couple had to borrow from family members and come up with a 20% down pay- ment and the additional required closing costs. Since Jacqueline and Keith had already accumulated significant credit card debt and were still paying off their college loans, they decided to opt for lower monthly payments by taking on a 30-year mortgage, despite its higher interest rate. Currently, due to worsening economic conditions, mortgage rates have come down significantly and a refinancing frenzy is underway. Jacqueline and Keith have seen 15-year fixed rates (with no closing costs) advertised at 2.75%, and 30-year rates at 3.75%. Jacqueline and Keith realize that refinancing is quite a hassle due to all the paperwork involved, but with rates being down to 30-year lows they don't want to let this opportunity pass them by. About two years ago, rates were down to similar levels, but they procrastinated and missed the boat. This time, however, the couple called their mortgage officer at the Uptown Bank and locked in the 2.75%, 15-year rate. Nothing was going to stop them from reducing the costs of paying off their dream house this time!

Explanation / Answer

5 years back, the Sommers chose to take a 30 Year mortgage loan with monthly payments @7.25%

The principal of the loan = 300,000-20% downpayment = 300,000-(20%*300,000) = $240,000

Let us now calculate the monthly payments Sommers are obligated to make under this mortgage loan:

Let C be the equal monthly payments done.n; o.of periods = 30*12=360 months; monthly rate=7.25/12%=0.604%  

Thus, the PV of this annuity of payments for n= 360 months @ r=0.604% per month should be equal to the principal of loan which is $240,000

240,000 = PV of annuity = C*(1-(1/(1+r)n)/r

240,000=C*(1-(1/(1.00604)360))/0.00604

-> C = $1,637.22

Sommers are considering to refinance the loan today at t= 5 years from the period of the original loan. Let us now calculate the Outstanding Loan Value today

Outstanding Loan Value today = PV of all the remaining cash flows of the 30-year mortgage loan

Since 5 years are passed, the remaining years left are 25

->Outstanding loan Value today = PV of the future 25 years of original loan payments = PV of annuity of $1,637.22 paid for n=25*12=300 months @0.604%

-> Outstanding Loan Value today = $226,509.07

Given the house is worth $355,000 today and lenders are willing to lend up to 90% of home value -> Sommers can borrow now as a part of refinancing the loan a maximum amount of 90% of $355,000 = $319,500

Out of this 90% amount borrowed, $226,509.07 amount is enough to replay the outstanding Loan Balance. Implying that the rest of the amount is an excess cash that Sommers can cash out as a part of refinancing the mortgage and can be used for other purposes.

Therefore, the cashout made by Sommers as a part of refinancing their original mortgage loan = $319,500 - $226,509.07

= $92,990.93

cashout made by Sommers = $92,990.93

(Note: In this problem, we basically won't be needing the refinancing loan values 15-year@2.75% rate to be used anywhere in the calculations.)

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