Question

Suppose that 10 years ago you bought a home for $170,000, paying 10% as a down payment, and financing the rest at 7% interest for 30 years. Your existing mortgage (the one you got 10 years ago)

How much money did you pay as your down payment?

How much money was your existing mortgage (loan) for?

What is your current monthly payment on your existing mortgage?

How much total interest will you pay over the life of the existing loan? $

This year (10 years after you first took out the loan), you check your loan balance. Only part of your payments have been going to pay down the loan; the rest has been going towards interest. You see that you still have $131,293 left to pay on your loan. Your house is now valued at $210,000. Your current situation

How much of the original loan have you paid off? (i.e, how much have you reduced the loan balance by? Keep in mind that interest is charged each month - it's not part of the loan balance.)

How much money have you paid to the loan company so far (over the last 10 years)? $ Note: the down payment is not included here, as it is paid directly to the seller

How much interest have you paid so far (over the last 10 years)?

How much equity do you have in your home (equity is value minus remaining debt) $ Submit Question Incorrect Question 9 Check 0/3 ptsRetries 1 Score on last try: 0 of 3 pts. See Details for more. You can retry this question below Refinancing Since interest rates have dropped, you consider refinancing your mortgage at a lower 6% rate. If you took out a new 30 year mortgage at 6% for your remaining loan balance, what would your new monthly payments be?

How much interest will you pay over the life of the new loan?

3 Analyzing the refinance Notice that if you refinance, you are going to be making payments on your home for another 30 years. In addition to the 10 years you've already been paying, that's 40 years total. How much will you save each month because of the lower monthly payment?

How much total interest will you be paying (consider the interest you paid over the first 10 years of your original loan as well as interest on your refinanced loan)

Does it make sense to refinance? (there isn't a correct answer to this question. Just give your opinion and your reason)

Answer 1

Given,

Cost of house= $170,000. Down payment=10%

Therefore, money paid as down payment= 170,000*10= $17,000

Existing mortgage loan= 170,000-17,000 = $153,000

Monthly payment on mortgage loan= $ 1,017.91   as follows:

Total payment over the life of loan= 1017.91*360 = $366,448.61

Therefore, total interest over the life of loan=$366,448.61-$153,000 = $213,448.61

Given, balance outstanding after 10 years= $131,293

Original loan paid off in 10 years= 153,000-131,293 = $21,707

Money paid so far during 10 years= 1,017.91*120 = $ 122,149.54

Interest paid over 10 years = 122,149.54 - 21,707 = $ 100,442.54

Given, Current valuation (after 10 years)=$210,000

Current equity in home= 210,000-131,293 = $78,707

New monthly payments (6%, 30 years loan) on new balance of $131,293= $787.17 as follows

Total payment over 30 years on the new loan= 787.17*360= $283,380.43

Therefore, total interest on the new loan= 283,380.43-131,293 = $152,087.43

Savings in monthly payment because of lower monthly payment= 1,017.91-787.17 = $230.74

Total interest (for both the loans together)= 100,442.54 + 152,087.43 = $252,529.97

If not refinanced, total interest paid would have been $213,448.61 as stated above. Upon refinancing, total interest for the whole life of the loan (40 years) is higher at $252,529.97. However, this is spread over additional 10 years. If not refinance, PV of the monthly payments of remaining 20 years at the new interest rate of 6% could have been $142,080.66 as follows:

This PV (ie., $142,080.66) is higher than the present balance of the loan being refinanced (ie., $131,293). Hence refinancing is beneficial.