Question

Some banks now have biweekly mortgages (that is, with payments every other week). Compare a 20-year, $100,000 loan at 7.5% by finding the payment size and the total interest paid over the life of the loan under each of the following conditions. (Round your answers to the nearest cent.)

(a) Payments are monthly, and the rate is 7.5%, compounded monthly.

payment size	$
total interest	$

(b) Payments are biweekly, and the rate is 7.5%, compounded biweekly. (Assume a standard 52-week year.)

payment size	$
total interest	$

Answer 1

Loan amount = $100000

loan period = 20 years

a). When interest rate is 7.5% compounded monthly,

Monthly payment can be calculated using PV formula of annuity

PMT = PV*(r/n)/(1 - (1+r/n)^(-n*t)) = 100000*(0.075/12)/(1 - (1 + 0.075/12)^(-12*20)) = $805.59

Payment size = $805.59

Total of monthly payment = PMT*total months = 805.59*12*20 = $193342.37

So, Interest paid = total of monthly payment - Loan amount = 193342.37 - 100000 = $93342.37

Total Interest = $93342.37

b). When interest rate is 7.5% compounded biweekly,

biweekly payment can be calculated using PV formula of annuity

PMT = PV*(r/n)/(1 - (1+r/n)^(-n*t)) = 100000*(0.075/26)/(1 - (1 + 0.075/26)^(-26*20)) = $371.54

Payment size = $371.54

Total of monthly payment = PMT*total months = 371.54*26*20 = $193202.49

So, Interest paid = total of monthly payment - Loan amount = 193202.49 - 100000 = $93202.49

Total Interest = $93202.49