Question

Five years ago you borrowed $100,000 to finance the purchase of a $120,000 house. The interest rate on the old mortgage is 10%. Payment terms are being made monthly to amortize the loan over 30 years. You have found another lender who will refinance the current outstanding loan balance at 8% with monthly payments for 30 years. The new lender will charge two discount points on the loan. Other refinancing costs will equal $3,000. There are no prepayment penalties associated with either loan. You feel the appropriate opportunity cost to apply to this refinancing decision is 8%.

a. What is the payment on the old loan?

b. What is the current loan balance on the old loan (five years after origination)?

c. What should be the monthly payment on the new loan?

d. Should you refinance today if the new loan is expected to be outstanding for five years?

Answer 1

a

Orginal monthly payment:

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		10.000%
Frequency of payment	=	Once in 1 month period
Numer of payments in a year	=	12/1 =	12
Rate of interest per period	R	0.1 /12 =	0.8333%
Total number of payments:
Frequency of payment	=	Once in 1 month period
Number of years of loan repayment	=	30
Total number of payments	N	30 × 12 =	360
Period payment using the formula	=	[ 100000 × 0.00833 × (1+0.00833)^360] / [(1+0.00833 ^360 -1]
Monthly payment	=	$                                                            877.57

b

Loan balance today:

Loan balance	=	PV * (1+r)^n - P[(1+r)^n-1]/r
Loan amount	PV =	100,000.00
Rate of interest	r=	0.8333%
nth payment	n=	60
Payment	P=	877.57
Loan balance	=	100000*(1+0.00833)^60 - 877.57*[(1+0.00833)^60-1]/0.00833
Loan balance	=	96,574.44

Balance is $96,574.44

c

Monthly payment	=	[P × R × (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Loan amount	P	$                                                            96,574
Rate of interest per period:
Annual rate of interest		8.000%
Frequency of payment	=	Once in 1 month period
Numer of payments in a year	=	12/1 =	12
Rate of interest per period	R	0.08 /12 =	0.6667%
Total number of payments:
Frequency of payment	=	Once in 1 month period
Number of years of loan repayment	=	30
Total number of payments	N	30 × 12 =	360
Period payment using the formula	=	[ 96574.44 × 0.00667 × (1+0.00667)^360] / [(1+0.00667 ^360 -1]
Monthly payment	=	$                                                            708.63

Monthly payment is $708.63

d

Period	Investment	× PV factor	Present value
0	$ 91,643	1	$ 91,642.95
1-60	-708.63	$49.32	$(34,948.52)
60	-91813.1	$0.67	$(61,625.92)
	NPV		$   (4,931.49)

NPV is negative it is better not to take the loan.