You plan to purchase a $350,000 house using either a 30-year mortgage obtained from your local savings bank with a rate of 8.20 percent, or a 15-year mortgage with a rate of 7.20 percent. You will make a down payment of 20 percent of the purchase price. You plan to purchase a $350,000 house using either a 30-year mortgage obtained from your local savings bank with a rate of 8.20 percent, or a 15-year mortgage with a rate of 7.20 percent. You will make a down payment of 20 percent of the purchase price.

a. Calculate the amount of interest and, separately, principal paid on each mortgage. What is the difference in interest paid?
b. Calculate your monthly payments on the two mortgages. What is the difference in the monthly payment on the two mortgages?

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.

* For option of mortgage obtained at the rate of 8.20%:

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.

* For option of mortgage obtained at the rate of 7.20%:

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.



(A) Amount of interest paid on MORTGAGE 30 is $473,706.8

Principal paid on MORTGAGE 30 is $280,000

Amount of interest paid on MORTGAGE 15 is $178,663.4

Principal paid on MORTGAGE 15 is $280,000

(B) Difference in interest paid on both mortgages is $295,043.4

(C) Monthly Payments on MORTGAGE 30 is $2,093.63

Monthly payments on MORTGAGE 15 is $2,548.13

(D) Difference in the monthly payments on both mortgages is $454.5

Explanation:

For MORTGAGE 30,

Annual Interest Rate=8.2%, Down Payment=20%, House Price=$350,000 Mortgage Period=30years

Monthly Interest Rate of the mortgage is r=[annual interest rate]÷12 = 8.2÷12 = 0.6833%

Number of months of the mortgage t=years of mortgage × 12 = 30×12=360

Loaned amount PV=house price × (1-down payment in %)

PV= $350,000 × (1-20%) = $350,000 × 0.8 = $280,000

Finally, monthly payments PMT=(0.6833% × $280,000) ÷ [1- (1+0.6833%)^-360]

PMT= 1913.24/0.9138 = $2,093.63

Principal paid =$280,000

Amount of interest= Total payments - Principal

Total Payments = $2,093.63 × 360 months = $753,706.8

Amount of interest= $753,706.8 - $280,000 = $473,706.8

For MORTGAGE 15,

Same format follows;

Monthly interest rate r = 7.2/12 = 0.6%

t = 15 years of mortgage × 12 months per year = 180 months

Loaned Amount PV=house price × (1-20%) = $280,000

PMT= 1,680/0.659 = $2,548.13

Principal= $280,000

Total payment = monthly payments × t = $2,548.13 × 180 = $458,663.4

Amount of Interest = $178,663.4

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