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
