Question

Value of the house 200,000. You are using a 30-year mortgage. Also, you are putting down 20%.

You have two options:

a. Mortgage rate of 4.5% with no points.

b. Mortgage rate of 4.35% and 1.5 points.

Which option should you choose?

Answer 1

a

Effective cost of loan is 4.5%

b

Loan amount = 160000 but amount received is = 160,000 - 160,000 * 1.5% = 157,600

Monthly payment	=	[P × R × (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Loan amount	P	$                                                          160,000
Rate of interest per period:
Annual rate of interest		4.350%
Frequency of payment	=	Once in 1 month period
Numer of payments in a year	=	12/1 =	12
Rate of interest per period	R	0.0435 /12 =	0.3625%
Total number of payments:
Frequency of payment	=	Once in 1 month period
Number of years of loan repayment	=	30.00
Total number of payments	N	30 × 12 =	360
Period payment using the formula	=	[ 160000 × 0.00363 × (1+0.00363)^360] / [(1+0.00363 ^360 -1]
Monthly payment	=	$                                                            796.50

Calculator
Inputs:
PV	157,600.000
PMT	(796.5)
FV	-
N	360
Output:
I/Y = YTM	0.3732%
Annual rate	4.48%

Take option 2 as effective cost of loan is lower at 4.48%