Home Mortgage (Chapter 3, 4: percents, compound interest, savings and loan formulas) In this project assume that you have a regular job, that you are planning to buy a house and that you want to investigate some of the financial aspects of buying a house and obtaining a mortgage. First, determine what criteria you desire in your house and then either contact a realtor or use the internet to find out the approximate cost of such a house. Then decide how much you can afford as a down payment and what you will need to borrow. Now, shop around for a mortgage, contacting at least two mortgage companies or banks (you can find this information on most websites), and find out: a) The APR for a 15 year loan, 20, 30 year loan, and for an adjustable rate mortgage; b) The total closing cost - you may want to get a truth and lending statement c) Determine the cost of mortgage insurance - can you afford a large enough down payment to eliminate mortgage insurance. With the above information, calculate the following for 2 mortgage companies/banks: a) The monthly payment on each of the 15 year loan, 20 year loan and the 30 year loan. Be sure to show your calculations. Does this agree with what the lender quoted? b) Next calculate the total cost of the 15 year loan, 20 year loan and the 30 year loan as well as how much you will pay in interest for each loan (in $ terms and % terms). c) If you could afford to pay an extra $250 a month toward your principle, estimate by trial and error (or see your instructor for an easier method) how long would it take you to pay off your mortgage. How much would you save in interest over the length of the loan? Would you be better off in the long run if you invested this $250 a month in a mutual fund or possibly invest that money in stocks/savings account or some other form of investment? Explain some possibilities. Now investigate the adjustable rate mortgage (ARM). What is ARM? What will your starting monthly payments be? What is the upper limit of the APR? How fast can it move to the upper limit and what would your monthly payments be if you did have to pay the upper limit on the APR? Research the information on web sites and report any useful information you find. Finally, summarize your findings as you examine the circumstances under each option and discuss what would be the most reasonable choice.

*I need the last question done, the one in bold, I got the data for this first part below.*

We are searching for an affordable mortgage loan for a family with a yearly income of $50,000 - $75,000 and a child on the way looking for a house near a school. As the search began a majority of single-family homes with 2-3 bedrooms ranged from $200,000 to $300,000. We have decided on a home that is $250,000, 3 bedroom, off of 700 east. Then we looked into different mortgage loans that would be best for our situation, specifically through Rocket Mortgage and University Credit Union, with a down payment amount of $15,000. We received results for a 30, 20, and 15 year mortgage loans through Rocket Mortgage that with a $15,000 down payment and $111.13 monthly insurance payment to help with the down payment due to the fact that most banks require a 20% down payment. For the 30 year loan we were quoted with a fixed rate at 4.375% and an APR of 4.859%, monthly payments of $1,474.85, with the closing cash amount of $14,581.12. The 20 year loan was quoted at a fixed rate of 4.625% and an APR of 5.004%, a monthly payment of $1,800.48, with the closing cash amount of $14,303.30. Lastly the 15 year loan quoted at a fixed rate of 4.625% an APR of 4.83%, a monthly payment of $2,023.50, and the closing cash amount of $14,909.46 From University Credit Union we received results for a 30, and 15 year mortgage loan with a down payment of $15,000 and insurance that adds a monthly payment of $155.38 to help provide for the down payment. The 30 year loan quoted us with fixed rate of 3.875% and an APR of 4.976%, monthly payments of $1,279.11 and closing fees of $22,497.13. The FHA 15 year loan quoted us with a fixed rate of 3.75% and an APR of 4.979%, monthly payments of $1,872.80 and closing cash amount of $22,496.31.

A) First quote 15 year monthly: [235,000 x (.0483/12)]/[1-(1+(.0483/12))^(-12x15)]=$1,837.62 20 year monthly: [235,000 x (.05004/12)]/[1-(1+(.05004/12))^(-12x20)]=$1,551.42 30 year monthly: [235,000 x (.04859/12)]/[1-(1+(.04859/12))^(-12x30)]=$1,241.36 Second quote 15 year monthly: [235,000 x (.04979/12)]/[1-(1+(.04979/12))^(-12x15)]=$1,855.80 30 year monthly: [235,000 x (.04976/12)]/[1-(1+(.04976/12))^(-12x30)]=$1,258.09

No it does not agree with what the lender quoted because we only used the APR with no closing costs.

B) First quote 15 year Total cost: 15 x 12 x 1,837.62= $330,771.60 Interest paid: 330,771.60-235,000=$95,771.60 Percent paid in interest: 29% 20 year Total cost: 20 x 12 x 1,551.42=$372,340.80 Interest paid: 372,340.80-235,000=$137,340.80 Percent paid in interest: 36.9% 30 year Total cost: 30 x 12 x 1,241.36=$446,889.60 Interest paid: 446,889.60-235,000=$211,889.60 Percentage paid in interest: 47.4% Second quote 15 year Total cost: 15 x 12 x 1,855.80= $334,044 Interest paid: 334,044-235,000= $99,044 Percentage paid in interest: 29.6% 30 year Total cost: 30 x 12 x 1258.09= $452,912.40 Interest paid: 452,912.40-235,000= $217,912.40 Percentage paid in interest: 48.1%

C)

I did this by finding the amount paid toward interest in each monthly payment through dividing the interest rate by the number of yearly payments (12) and multiplying that number by the remaining principal each month. This will tell you how much of the monthly payment goes towards interest each month, and the remaining amount is subtracted from principal as well as an additional $250.

(.0483/12)xP = iPMT (this is amount paid toward interest for the monthly payment)

PMT - iPMT = PP (principal payment)

P - (PP + 250) = P next month

I was then able to extrapolate this across each monthly payment to find these results:

First quote: 15 year: By paying an extra $250 (now $2,087.62) per month the mortgage will be paid off in 12 years and 7 months, saving $17,145.44 in interest payments.

20 year: By paying an extra $250 (now $1,801.42) per month the mortgage will be paid off in 15 years and 9 months saving $32,413.50 in interest payments.

30 year: By paying an extra $250 (now $1,491.36) per month the mortgage will be paid off in 21 years, saving $71,837.94 in interest payments.

Second quote: 15 year: By paying an extra $250 (now $2,105.80) per month the mortgage will be paid off in 12 years and 7 months, saving $17,800.54 in interest payments.

30 year: By paying an extra $250 (now $1,508.09) per month the mortgage will be paid off in 21 years, saving $74,288.17 in interest payments.

In each of these mortgages and their respective time periods we would be better off saving this extra $250/month. With investment, we have the opportunity to grow our money to even greater amounts but we could also lose the money. I would recommend a low risk investment that can give us low % returns over a long period of time, or to simply save the monthly $250

Quote 1 - 15 year: $250x12x15 = $45,000 > saved interest amount of $17,145.44 Quote 1 - 20 year: $250x12x20 = $60,000 > saved interest amount of $32,413.50 Quote 1 - 30 year: $250x12x30 = $90,000 > saved interest amount of $71,837.94

Quote 2 - 15 year: $250x12x15 = $45,000 > saved interest amount of $17,800.54 Quote 2 - 30 year: $250x12x30 = $90,000 > saved interest amount of $74,288.17

Overall, saving or investing this monthly $250 will be more efficient than applying it to the mortgage. If we consider inflation, I would say that the most efficient use of the monthly $250 at the 30 year level goes as follows

(best) Monthly investment > Mortgage > Saving (worst)

Please help with the part in bold with the data below it. Thank you!