Question

A borrower is making a choice between a mortgage with monthly payments or biweekly payments. The loan will be $200,000 at 6% interest for 20 years. How would you analayze these alternatives?

Answer 1

The PMT for the two alternatives would be using the formula for loan amortization as below:
PMT = L*[(r/12)*(1+r/12)]^(n*12)/[(1+r/12)^(n*12)-1
Where,
L = loan amount, r=annual interest in decimals and n = number
of mortgage years.
r/12 gives monthly interest in decimals; for biweely it is
r/52 and n*52.
PMT for Monthl payments:
PMT = 200000*[(0.06/12)*(1+0.06/12)^(20*12)]/[(1+0.06/12)^(20*12)-1] =	$          1,432.86
PMT for biweekly payments:
PMT = 200000*[(0.06/26)*(1+0.06/26)^(20*26)]/[(1+0.06/26)^(20*26)-1] =	$              660.86
ANALYSIS:	Monthly	Bi-weekly
Total payment towards interest and principal
=1432.86*20*12 =	$    3,43,886.40
= 660.86*20*26 =		$   3,43,647.20
Principal repayment	$    2,00,000.00	$   2,00,000.00
Amount paid towards interest	$    1,43,886.40	$   1,43,647.20
Effective annual interest:
= (1+0.06/12)^12-1 =	6.17%
= (1+0.06/26)^26-1 =		6.18%
COMMENTS:
The interest difference in total is marginal. What is relevant is the frequency of payments, monthly
or bi-weekly, which the mortgagee should choose.