Part I
Compound Interest: Mortgages and Investments
The retirement goals of most Americans include a paid-for home and a nest egg for investment income. In this assignment you will consider a couple of scenarios in which you pay off a home mortgage and invest for retirement over a 30-year period. And whether its paying a loan or investing in an annuity, compound interest plays a key role. As we will see in this assignment, the "magic" of compound interest can either work for you or against you; understanding the math involved can quite literally mean the difference between retiring a millionaire and praying that Social Security lasts long enough.
As you begin your career and think about starting a family, you decide to purchase a home with a $200,000 mortgage loan. While there are many factors that must be taken into account, here we consider two basic options. (Refer to the Example of Calculating Mortgage Payments handout for details on the necessary computations.)
1. Suppose you are considering a 30-year fixed-rate mortgage.
(a) The website www.freddiemac.com/pmms/pmms30.htm contains data from the Primary Mortgage Market Survey, and lists historical interest rate information for loans of the type you are considering. Go to this website and locate the "Annual Average" rate for a 30-year fixed-rate mortgage in 2013.
(b) Using the interest rate found in part (a), determine the monthly payment on this mortgage.
(c) What would be the total amount required to pay off the loan?
(d) How much total interest would you pay?
2. You have heard that there are benefits to paying off your house sooner, so you decide to compare the above 30-year mortgage to a shorter 15-year loan.
(a) The website www.freddiemac.com/pmms/pmms15.htm lists historical interest rate information for loans of this type. Go to this website and locate the "Annual Average" rate for a 15-year fixed-rate mortgage in 2012.
(b) Using the interest rate found in part (a), determine the monthly payment on this mortgage.
(c) What would be the total amount required to pay off the loan?
(d) How much total interest would you pay?
3. Compare your results from questions 1 and 2 to answer the following:
(a) How much more (or less) would you pay per month on the 15-year loan?
(b) How much more (or less) would you pay over the life of the 15-year loan compared to the 30-year mortgage?
4. Write a 3-5 sentence paragraph describing which of the above methods of payment you would choose. Incorporate your answers from the previous questions. Also take into account any other considerations you may have, such as current lifestyle versus future lifestyle. (Would you rather pay less now so that you have more to spend, or spend less now to pay off the loan and free up that money sooner?)
Part II
Compound Interest: Mortgages and Investments
Now it's time to start investing for retirement. Certain financial experts suggest that you should spend a total of approximately one third of your net income (take-home pay) on both housing and investments. You would like to have enough money to retire in 30 years, and decide to make a plan for retirement investing. You will pay your mortgage payment from the suggested third of your income, and then invest the remainder each month in an annuity.
You decide to compare the two mortgage options described in Part I again by applying your investment plan to each. You will calculate the predicted value of your investments in each case at 5-year intervals, then graph your results, and finally report on your findings.
5. Suppose your household annual net income is $54,000. According to the above information, how much should you spend each month on housing and investments?
6. The handout Dow Jones Historical Data gives information on index prices and annual percentage change of the Dow Jones Industrial Average from 1992 to 2012. Use this data to determine the average annual percentage change of the Dow Jones Industrial Average over this time period. (To do this, simply find the average of the given percentage changes.) This number will be your estimate for the annual rate of return you may expect from your retirement investments.
For questions 7 and 8, refer to the Calculating Investment Income slideshow, which details the computations involved with investments of the type we consider in this assignment.
7. Suppose you choose the 30-year mortgage described in question 1 of Part I.
(a) Use your answers from 1(b) and question 5 above to determine how much you would have availabe to invest each month, while paying off your mortgage.
(b) Assuming you start investing and paying off your mortgage loan today, what would be the value of your investments in
(1)5 years?
(2)10 years?
(3)15 years?
Continuing this process gives the following results:
(4) After 20 years, the investments' value is $362,931.96.
(5) After 25 years, the investments' value is $595,774.22.
(6) After 30 years, the investments' value is $950,160.54.
8. Now, suppose you choose the 15-year mortgage described in question 2 of Part I. (Note that, per your investment plan, once you finish paying off your mortgage, you will begin investing the entire one third of your income for the remainder of the 30 year period. Since this requires slightly more complicated calculations, the answers for years 20, 25, and 30 are given below.)
(a) Use your answers from 2(b) and question 5 above to determine how much you would have availabe to invest each month, while paying off your mortgage.
(b) Assuming you start investing and paying off your mortgage loan today, what would be the value of your investments in
(1) 5 years?
(2) 10 years?
(3) 15 years?
At the end of 15 years, you have paid off your mortgage, and then invest the full one-third of your income each month for the remaining 15 years. Here are the results obtained:
(4) After 20 years, the investments' value is $180,166.59.
(5) After 25 years, the investments' value is $385,673.30.
(6) After 30 years, the investments' value is $698,454.86.
9. OMIT
10. Will you end up with a bigger nest egg if you have a lower mortgage payment and invest more now, or if you finish paying off your mortgage sooner, freeing up that money for investing? Under this investment plan, would you choose the 30-year mortgage or the 15-year loan? Why? Defend your results in a well-written, 3-5 sentence paragraph, citing relevant numerical results from previous questions in the assignment.
Dow Jones Industrial Average
Historical Data for 1992-2012
| Year |
Closing Price on First Business Day of December |
Percentage Change from Previous Year |
| 1992 |
3301.11 |
|
| 1993 |
3754.09 |
13.72% |
| 1994 |
3834.44 |
2.14% |
| 1995 |
5117.12 |
33.45% |
| 1996 |
6448.27 |
26.01% |
| 1997 |
7908.3 |
22.64% |
| 1998 |
9181.43 |
16.10% |
| 1999 |
11497.12 |
25.22% |
| 2000 |
10787.99 |
-6.17% |
| 2001 |
10021.5 |
-7.11% |
| 2002 |
8341.63 |
-16.76% |
| 2003 |
10453.92 |
25.32% |
| 2004 |
10783.01 |
3.15% |
| 2005 |
10717.5 |
-0.61% |
| 2006 |
12463.15 |
16.29% |
| 2007 |
13264.82 |
6.43% |