Question

You will stay at a house for at most 10 years after buying it before selling it. When buying the house, you took a 10- year-ARM mortgage from a bank. The APR of the mortgage is 4%. The rate is expected to rise to 4.75% after the 10-year (from the origination of the mortgage) period. The remaining balance is $1 million. Noticing that the mortgage rates decrease recently, you are considering whether to refinance your mortgage or not. To make a more informed decision, you contacted a few mortgage brokers. From these brokers, the best options you find are the following.

Option 1: 30 years fixed-rate mortgage with an APR of 4%. The closing fee is $4000.

Option 2: 10 year ARM with and APR of 3.875%. The closing fee is $1000.

Option 3: 10 year ARM with and APR of 3.75%. The closing fee is $8000.

Besides looking into these options, you are also aware that all the interest rates have a 50% chance to increase by 0.5%, and a 50% chance to drop by 0.25% in half a year (when you can refinance again). Are you going to refinance your mortgage now? If yes, which option would you choose and what is the benefit (in $ amount)? Please explain the reason behind your choice.

Answer 1

10- year-ARM mortgage taken at APR of 4%

ARM is adjustable rate of mortgage and APR is annual percentage rate .

we will refinance only if rate will decrease and benefited after fees.

Option 1: 30 years fixed-rate mortgage with an APR of 4%. The closing fee is $4000

50% chance that rate will increase by 0.5% and 50% chance that it will decrease by 0.25% in half year

Total benefit = [ ( 0.5 * (0.005(1/2))) - (0.5*(0.0025(1/2)))]* $1000000 = $625 - $4000 = -$3375 in half year

Option 2: 10 year ARM with and APR of 3.875%. The closing fee is $1000

50% chance that rate will increase by 0.5% and 50% chance that it will decrease by 0.25% in half year

Total benefit = { [ (0.04-0.03875)(1/2) + (0.5 *(0.0025(1/2))) - (0.5*0.005(1/2)] * $1000000} = 0%*1000000 = 0 - $ 1000 = -$1000 in half year

Option 3: 10 year ARM with and APR of 3.75%. The closing fee is $8000

50% chance that rate will increase by 0.5% and 50% chance that it will decrease by 0.25% in half year

Total benefit = { [ (0.04-0.0375)(1/2) + (0.5 *0.0025(1/2)) - (0.5*0.005(1/2))] * $1000000} = 0.00125 * $1000000 = $ 625 -$ 8000  = - $7375 in half year

NO

we will not  refinance under any option   because if we wont refinance under any option we will have loss =(0.50* 0.005(1/2)) - ( 0.5 * 0.0025(1/2)) =0.00125*$1000000 = $625 loss in half year.