Question

Part II -Mortgage Refinance Suppose your friend April is considering to refinance her mortgage. She bought her house 60 months ago. The amount of loan equals 154,000. She paid cash to cover the 5% down payment plus all required closing costs (closing costs include application fee, appraisal fee, loan origination fees and other costs, usually about 3%-5% of the loan amount). Since she had a decent credit history and relatively stable income, her mortgage rate was 5.25% for 30 years at the time of the purchase. Since her down payment was less than 20%, she had to pay monthly mortgage insurance premium which is $80 per month (premiums are automatically terminated when the LTV ratio (loan-to-value ratio) falls below 80%). Recently, mortgage rate has been dropping and she is considering to refinance her mortgage. She talked with a mortgage banker and got the following information: a) 3.75% 30 year conventional loan with out-of-pocket closing costs of $1,800 b) 3.5% 30 year conventional loan with out-of-pocket closing costs of $3.000; c) 3.25% 30. year conventional loan with out-of-pocket closing costs of $4,000. Based on the recent appraisal, her house value has changed to $180,000. Please advise her on the following: 1) How much should her monthly payment be under each option (a, b, and c)? Show your calculations. 2) Would you suggest her to do the refinancing or not? Why? Notice that monthly payment is reduced but she need to make 360 payments plus closing costs under the new mortgage versus 300 payments in the old mortgage. 3) Which option would you suggest her to take? What factors would affect her choice and how?

Answer 1

formula for EMI(monthly installment)= [P*R*(1+R)^N]/[(1+R)^N-1]

where P=Principal, R=Rate of interest per month, N=number of installment monthly.

EMI under original mortgage is as under:

	House cost	154000
Less:	down payment	-7700		after 5 years
	Loan Amount	146300		balance principal	134814.7
	Loan Duration	30 years		Interest paid in first 5 years	36720.5
	interest	5.25%		interest to be paid in next 5 years	107814.2
	EMI	807.87
	Principal	146300
	interest	144534.65
	Total	290834.65

Answer to Q1: Monthly payment under each option a, b and C

EMI= [P*R*(1+R)^N]/[(1+R)^N-1]

where P=Principal, R=Rate of interest per month, N=number of installment monthly.

		Option A	Option B	Option C
	principal	134815	134815	134815
	interest	3.75%	3.50%	3.25%
	loan duration	30	30	30
	EMI	624	605	587
	Interest Total	89,951	83,122	76,405
	Out of pocket Cost	1,800	3,000	4,000
	Total Cost	91,751	86,122	80,405

Ans to Q2. Yes refinancing should be done as total future interest payment will reduce despite increase in duration under all three new options.

Ans to Q3. Option C is best and should be selected as it has lowest total cost (interest + out of pocket cost) which is coming to 80,405