1 MATH'S PROBLEMS [Insert Name] [Institution Affiliation] 2 Suppose that 10 years ago you bought a home for $110,000, 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) Question 1. How much money did you pay as your down payment? 10% * 110000= 11000 $ 11000 Question 2. Points: 0 out of 1 possible. How much money was your existing mortgage (loan) for? $(110000- 11000)= $ 99000 Question 3. Points: 0 out of 3 possible. What is your current monthly payment on your existing mortgage? Let P be the monthly payment, R= 0.07/12=0.0058 N=12(30)=360 P (1-((1+0.0058) ^-360)) =99000 P=99000/151=655.99 = $ 656 Question 4. Points: 0 out of 2 possible. How much total interest will you pay over the life of the existing loan? 656*240=157440-99000 $ 58440 Question 5. Points: 0 out of 1 possible. 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 $84,954 left to pay on your loan. Your house is now valued at $150,000. 3 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.) $ (99000-84954) $14046 Question 6. Points: 0 out of 1 possible. How much money have you paid to the loan company so far (over the last 10 years)? 1-(1+0.0058)^-120)/0.0058=99000 P=1147(120)= 137692 $ 137692 Question 7. Points: 0 out of 1 possible. How much interest have you paid so far (over the last 10 years)? $ (137692-99000) = 38692 Question 8. Points: 0 out of 1 possible. How much equity do you have in your home (equity is value minus remaining debt) $ 150000-137160=$12840 Question 9. Points: 0 out of 3 possible. Refinancing Since interest rates have dropped, you consider refinancing your mortgage at a lower 6% rate. If you took out a new 30 year mortgage at 6% for your remaining loan balance, what would your new monthly payments be? r=6%/12=0.005 N=12*30=360 P(1-(1+0.005)^-360/0.005=99000 New monthly payments =$ 594 Question 10. Points: 0 out of 2 possible. 4 How much interest will you pay over the life of the new loan? $ (594*360-99000) =114840 Question 11. Points: 0 out of 1 possible. 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? $ (656-594) =62 Question 12. Points: 0 out of 1 possible. 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) $ (114840+38692)=153532 Question 13. Points: 0 out of 2 possible. Now the non-computational question: Does it make sense to refinance? (there isn't a correct answer to this question. Just give your opinion and your reason) It absolutely makes sense to refinance owing to the fact that it reduces the interest rates of servicing the loan hence making it affordable and at the same worthy since you will be saving each month a considerable amount ($62)