Answer:
a.
* The option of mortgage obtained at the rate of 8.20%:
+ Principal paid: $280,000
+ Interest paid: $473,735.6
* The option of mortgage obtained at the rate of 7.20%:
+ Principal paid: $280,000
+ Interest paid: $178,658
b.
Monthly payment for the option of mortgage obtained at the rate of 8.20%: $2.093.71
Monthly payment for the option of mortgage obtained at the rate of 7.20%: $2,548.1
The difference on monthly payment between the two option is: $454.39
Explanation:
For both options, we will have to borrow 80% of the house's price because the down payment is 20% or we have to borrow 350,000 x 80% = $280,000 => The principal needs to be paid for two options is the same, $280,000.
<u>* For option of mortgage obtained at the rate of 8.20%:</u>
We apply the present value of annuity formula to find the interest rate paid and monthly payment with discount rate of 8.2%/12 and discounting period of 12*30 = 360
we have: 280,000 = PMT/(8.2%/12) * [ 1 - (1+8.2%/12)^-360] <=> PMT = $2.093.71
=> There is a total of 2.093.71 x 360 = $753,735.6 repayment has been made, with $280,000 is for principal repayment => Interest expenses paid = 753,735.6 - 280,000 = $473,735.6.
<u>* For option of mortgage obtained at the rate of 7.20%:</u>
We apply the present value of annuity formula to find the interest rate paid and monthly payment with discount rate of 7.2%/12 = 0.6% and discounting period of 12*15 = 180
we have: 280,000 = PMT/(0.6%) * [ 1 - (1+0.6%)^-180] <=> PMT = $2,548.1
=> There is a total of 2,548.1 x 180 = $458,658 repayment has been made, with $280,000 is for principal repayment => Interest expenses paid = 458,658 - 280,000 = $178,658.
