Question

Suppose you currently have 25 years remaining on a mortgage that started as a $200,000, 30-year 6% mortgage. Your current balance is $186,108.71. Your current payment (including both principal and interest) is $1,199.10. Ignoring closing costs, evaluate whether you should refinance into a 30-year 5%mortgage or a 15-year 4% mortgage. Determine the following for both alternatives:

a. What would be the new monthly payment assuming you refinance the existing balance of $186,108.71?

b. What would be the total accumulated interest savings over the life of the mortgage (the total interest costs of the new mortgage minus the total interest costs of the existing mortgage) ignoring differences in the time value of money?

c. What factors will you take into account for your alternatives?

Answer 1

Part a) For the new 30 year loan, the monthly payment is calculated as follows:

We are given the following information:

r	5.00%
n	30
frequency	12 (monthly)
PV	$   1,86,108.71

We need to solve the following equation to arrive at the required PMT:

So the Monthly payment is 999.07

For the new 15 year loan, the monthly payment is calculated as follows:

We are given the following information

r	4.00%
n	15
frequency	12
PV	$   1,86,108.71

We need to solve the following equation to arrive at the required PMT:

So the monthly payment is 1376.62

b) Accumulated savings on interest is calculated below

Particulars	Existing	New 30 Year	New 15 year
Year Remaining	25	30	15
Number of payments per year	12	12	12
Total payments remaining	300	360	180
Monthly payment	$         1,199.10	$             999.07	$         1,376.62
Principal	$   1,86,108.71	$   1,86,108.71	$   1,86,108.71
Total payments	$   3,59,730.32	$   3,59,665.85	$   2,47,792.26
Interest	$   1,73,621.61	$   1,73,557.14	$       61,683.55
Savings		$               64.47	$   1,11,938.06

• New 30 Year leads to a savings of $ 1,73,621.61 - $ 1,73,557.14 = 64.47
• New 15 Year leads to a savings of $ 1,73,621.61 - $ 61,683.55 = 1,11,938.06

C)

• We see that the monthly payments are higher for 15 year loan than the 30 year loan so is it possible to make such payments need to be analysed.
• Further the time taken to pay off the loan is just half in one alternative, so is that what the borrower wants because if the loan doesn't need to be paid off earlier then it is not advisable to pay it earlier using today's dollars because a dollar now is worth more than that later.
• Interest savings from both the alternatives is a big difference and needs to be considered