Question

 

You apply for a 15-year, fixed-rate (APR 4.08%) monthly-payment-required mortgage loan for a house selling for $120,000 today. Your bank requires 22% initial down payment of house value (to be paid upfront in cash immediately, thus not included in the loan balance), therefore lends you the remaining 78% of house value as the loan, plus $3,000 application-process-closing cost (to be added into the beginning loan balance and amortized later).   

(a) What is your monthly loan payment if you stick to the mortgage deal till the end, assuming each payment is made at the end of each month?  

(b) 6 years (i.e., 72 months, please note again that it is a monthly mortgage) after buying the house, what will be the remaining loan principal balance?

(c) 6 years (i.e., 72 months) after buying the house, the mortgage loan market rate drops from 4.08% APR to 3.48% APR. You think about the option of refinancing to save money, but do not want to do the 15-year mortgage all over again, only want to refinance on the remaining loan principal balance for the remaining loan life period. Refinancing is not free, because the bank would charge an extra refinancing fee of $4,500, to be added into the remaining loan principal balance for amortization later. If you choose to refinance, would you be able, and by how much, to lower your monthly loan payment and thus save money? Based on your calculation results, should you choose to refinance or not?

(d) Redo the calculations in Question (c), assuming that the loan market rate drops from 4.08% APR to 3.72% APR (instead of 3.48%). Should you refinance or not then?

Answer 1

a)
Cost of House	$ 120,000.00
Less: Down payment	$   26,400.00
Amount Borrowed	$   93,600.00
Application Process fee	$     3,000.00
Total Amount Borrowed = PV	$   96,600.00
Monthly Rate = 4.08%/12	0.34%
Period = 15 years x 12	180
FV	0
Type	0
Monthly Payment = PMT	$718.42
b)
Total Amount Borrowed = PV	$   96,600.00
Monthly Rate = 4.08%/12	0.34%
Period = 6 years x 12	72
FV	0
Type	0
Loan principal balance at end 6th year or 72 months	$64,847.18
c)
Loan refinanced =	$64,847.18
Refinancing fee	$     4,500.00
Total Amount Borrowed = PV	$   69,347.18
Monthly Rate = 3.48%/12	0.29%
Period = 9 years x 12	108
FV	0
Type	0
Monthly Payment = PMT	$748.82
There is no saving in monthly payment so refinancing is not a good idea.
d)
Loan refinanced =	$64,847.18
Refinancing fee	$     4,500.00
Total Amount Borrowed = PV	$   69,347.18
Monthly Rate = 3.72%/12	0.31%
Period = 9 years x 12	108
FV	0
Type	0
Monthly Payment = PMT	$756.56
There is no saving in monthly payment so refinancing is not a good idea.