Question

a borrower takes out a 15 year mortgage loan for 100,000 with an interest rate of 5% plus 3 points. what is the effective annual interest rate on the loan if the loan is carried 15 years.

Answer 1

Monthly payment	=	[P × R × (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Loan amount	P	$                                                          100,000
Rate of interest per period:
Annual rate of interest		5.000%
Frequency of payment	=	Once in 1 month period
Numer of payments in a year	=	12/1 =	12
Rate of interest per period	R	0.05 /12 =	0.4167%
Total number of payments:
Frequency of payment	=	Once in 1 month period
Number of years of loan repayment	=	15.00
Total number of payments	N	15 × 12 =	180
Period payment using the formula	=	[ 100000 × 0.00417 × (1+0.00417)^180] / [(1+0.00417 ^180 -1]
Monthly payment	=	$                                                            790.79

Effective cost
Loan received PV	PV	97,000
Monthly payment	PMT	$                                                                           (790.79)
Closure amount	FV	0.00
Number of paymnets	N	180.00
Effective cost (I/Y)	I/Y	0.46%
Effective cost APR		5.47%

Answer is 5.47%