Question

The Home section of many Sunday newspapers includes a mortgage table similar to the one below-The table gives the monthly payment per $ 1000 borrowed for loans at various interest rates and time periods. Interest 15-year 20-year 2 rate (%) | loan 25-year 30-year loan loan 4.00 7.406.065.28 4.77 4.50 7.656.335.56 5.07 5.00 7.916.60 5.85 5.37 5.50 8.176.886.14 5.68 6.00 8.4 7.16 6.44 6.00 6.50 8.77.466.75 6.32 7.00 8.997.75 7.07 6.65 7.50 9.278.067.39 6.99 7.34 8.00 9.56 8.36 7.72 (a) (i) Determine the monthly payment on a $ 80,000 mortgage at 6% for fifteen years. (ii) Determine the monthly payment on a $ 80,000 mortgage at 6% for thirty years. (iii) Determine the monthly payment on a $ 80,000 mortgage at 8% for fifteen years. (b) Over the life of the loan, how much money would be saved on a 15-year mortgage of $ 80,000 if the rate were 6% instead of 8%? (c) Over the life of the loan, how much money would be saved on a 6% mortgage of $ 80,000 if the term of the loan was fifteen years rather than thirty years?

Answer 1

(a)

(i)

For 15-year loan at 6% interest rate, person has to pay $8.44 for per $1,000 borrowed.

If $80,000 is borrowed then monthly payment would be,

Monthly payment = $8.44 * 80 = $675.20

The monthly payment would be $675.20.

(ii)

For 30-year loan at 6% interest rate, person has to pay $6.00 for per $1,000 borrowed.

If $80,000 is borrowed then monthly payment would be,

Monthly payment = $6.00 * 80 = $480

The monthly payment would be $480.

(iii)

For 15-year loan at 8% interest rate, person has to pay $9.56 for per $1,000 borrowed.

If $80,000 is borrowed then monthly payment would be,

Monthly payment = $9.56 * 80 = $764.80

The monthly payment would be $764.80.

(b)

If rate is 6% then monthly payment for 15 year mortgage of $80,000 is $675.20. There are 180 months in 15 years.

So,

Total amount repaid = $675.20 * 180 = $121,536

If the rate is 8% then monthly payment for 15 year mortgage of $80,000 is $764.80

So,

Total amount repaid = $764.80 * 180 = $137,664

Amount saved = $137,664 - $121,536 = $16,128

Thus,

Over the life of loan, total amount saved would be $16,128.

(c)

If rate is 6% then monthly payment for 15 year mortgage of $80,000 is $675.20. There are 180 months in 15 years.

So,

Total amount repaid = $675.20 * 180 = $121,536

If rate is 6% then monthly payment for 30-year mortgage of $80,000 is $480. There are 360 months in 30 years.

So,

Total amount repaid = $480 * 30 = $172,800

Amount saved = $172,800 - $121,536 = $51,264

Thus,

Over the life of loan, total amount saved would be $51,264.