Question

On the following real estate mortgage loan, what is the best estimate of the effective borrowing cost if the loan is prepaid in 6 years?

Loan: $100,000
Interest rate: 7 %
Term: 180 months
Up-front costs: 7 % of loan amount

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		7.000%
Frequency of payment	=	Once in 1 month period
Numer of payments in a year	=	12/1 =	12
Rate of interest per period	R	0.07 /12 =	0.5833%
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 × 0.00583 × (1+0.00583)^180] / [(1+0.00583 ^180 -1]
Monthly payment	=	$                                                            898.83

Loan balance	=	PV * (1+r)^n - P[(1+r)^n-1]/r
Loan amount	PV =	100,000.00
Rate of interest	r=	0.5833%
nth payment	n=	72
Payment	P=	898.83
Loan balance	=	100000*(1+0.00583)^72 - 898.83*[(1+0.00583)^72-1]/0.00583
Loan balance	=	71,870.17

Loan amount received = 100,000 * (1-7%) = 93,000

Effective cost is:

Effective cost
Loan received PV	PV	93,000
Monthly payment	PMT	$                                                                           (898.83)
Closure amount	FV	(71,870.17)
Effective cost (I/Y)	I/Y	0.73%
Effective cost APR		8.70%

Answer is 8.70%