Question

1. Suppose that 10 years ago you bought a home for $150,000, paying 10% as a down payment, and financing the rest at 8% interest for 30 years. How much money did you pay as your down payment?
2. How much money was your existing mortgage (loan) for?
3. What is your current monthly payment on your existing mortgage? Note: Carry at least 4 decimal places during calculations, but round your final answer to the nearest cent.
4. How much total interest will you pay over the life of the existing loan?
5. 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 $112,681 left to pay on your loan. Your house is now valued at $180,000.
6. How much of the original loan have you paid off (i.e, how much have you reduced the loan balance by?
7. How much money have you paid to the loan company so far (over the last 10 years)?
8. How much interest have you paid so far (over the last 10 years)?
9. How much equity do you have in your home (equity is value minus remaining debt)?
10. 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?
11. 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?
12. 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)?
13. Now the non-computational question: Does it make sense to refinance?

Answer 1

Answer:

1. Down payment = $15,000

2. The existing mortgage (loan) was for $135,000

3. The current monthly payment on the existing mortgage is $990.58

4. The total interest over the life of the existing loan = $221,609.58

6. The amount of the original loan paid off is $22,319.

7. Total amount paid to the loan company over the last 10 years is $258,928.58 ($243,928.58 + $15,000)

8. Total interest paid over the last 10 years is $221,609.58

9. The equity in the home is $67,319 ($180,000 - $112,681)

10. The new monthly payments will be $675.58

11. Saving each month because of the lower monthly payment is $315 ($990.58 - $675.58)

12. Total Interest = $352,137.21 ($221,609.58 + $130,527.63)

13. It does not make sense to refinance because what is saved per month cannot compare with the additional interest expense to be incurred for prolonging the payments.

Explanation:

a) Data and Calculations:

1. Cost of a home = $150,000

10% down payment = $15,000

Existing Mortgage = $135,000 ($150,000 - $15,000)

Home Price  150000

 Down Payment  10 %

Loan Term  30  years

Interest Rate  8%

House Price $150,000.00

Loan Amount $135,000.00

Down Payment $15,000.00

Total of 360 (30 years * 12)

Mortgage Payments $356,609.58

Total Interest $221,609.58

Ten years after, the loan balance has been reduced by $22,319 ($135,000 - $112,682)

Refinancing calculations:

Home Price  112681

 Down Payment  0 %

Loan Term  30  years

Interest Rate  6

   

Monthly Pay:   $675.58 Monthly

Total Mortgage Payment $243,208.63

Total Out-of-Pocket $243,208.63

Total of 360 Mortgage Payments $243,208.63

Total Interest $130,527.63