Question

Alice is buying a house with 625K. She is making 20% deposit. And get a mortgage on the balance.A bank offers her two options.

Answer 1

Answer:

By opting for the second option, Alice would save $ 15,740.00  in total mortgage cost

Step-by-step explanation:

In order to determine the better of the two options available, we need to determine the total cost under each option as follows:

Option 1:

cost of house=$625,000

loan amount=$625,000-(20%*$625,000)=$500,000

loan amount=monthly payment*(1-(1+r)^-n/r

monthly payment is the unknown

r=monthly interest rate=4%/12=0.33333333%

n=number of monthly payments in 30 years=30*12=360

500,000=monthly payment*(1-(1+0.33333333% )^-360/0.33333333%

500,000=monthly payment*(1-0.301795869 )/0.003333333

500,000=monthly payment*0.698204131 /0.003333333

monthly payment=500,000*0.003333333 /0.698204131

monthly payment=$ 2,387.08  

total monthly payments=$ 2,387.08*360=$859,348.80

Option 2:

upfront fee=$10,000

loan amount=monthly payment*(1-(1+r)^-n/r

monthly payment is the unknown

r=monthly interest rate=3.75%/12=0.3125%

n=number of monthly payments in 30 years=30*12=360

500,000=monthly payment*(1-(1+0.3125%  )^-360/0.3125%

500,000=monthly payment*(1-0.325222459  )/0.003125

500,000=monthly payment*0.674777541  /0.003125  

monthly payment=500,000*0.003125  /0.674777541=$2,315.58  

Total cost=total monthly payments+upfromt fee

total cost=($2,315.58 *360)+$10,000=$843,608.80  

savings by opting for the second option=$859,348.80-$843,608.80