Question

Jackie bought a $200,000 house and has a 30 year mortgage at a nominal interest rate of 4.8% convertible monthly. Jackie must pay level payments at the end of each month. Find the amount of her monthly mortgage payment. After 200 payments have been made, what is the ratio of total interest paid to total principal repaid?

Answer 1

Jackie bought a $200,000 house and has a 30 year mortgage at a nominal interest rate of 4.8% convertible monthly. Jackie must pay level payments at the end of each month. Find the amount of her monthly mortgage payment. After 200 payments have been made, what is the ratio of total interest paid to total principal repaid?

Loan amount taken for house = $200,000

Calculating the monthly Loan amount:-

Where, P = Loan amount = $200,000

r = Periodic Interest rate = 4.8%/12 = 0.4%

n= no of periods = 30 years*12 = 360

Monthly Payment = $1049.33

So, the amount of her monthly mortgage payment is $1049.33

b). Calculating the Loan Balnace after 200 payments:-

Where, P = Loan amount = $200,000

r = Periodic Interest rate = 4.8%/12 = 0.4%

n= no of periods = 30 years*12 = 360

m = no of loan payments already made = 200

Outstanding Loan Balance = $123,829.94

- Total Principal Repaid till 200th paymnet = Loan amount - Outstanding Loan Balance

= $200,000 - $123,829.94

Total Principal Repaid till 200th payment = $76,170.06

- Total Interest paid till 200th payment = (Monthly Paymnet*No of payments) - Total Principal Repaid till 200th paymnet

= ($1049.33*200) - $76,170.06

Total Interest paid till 200th payment = $133,695.94

So, the ratio of total interest paid to total principal repaid = $133,695.94/$76,170.06

= 1.7552 times