Assignment

CASE STUDY: THE AMAZING IMPACT OF COMPOUND INTEREST

Background on Five Situations

1. The first mass produced automobile was the Ford Model T, initially manufactured and sold in 1909 for $825. The rate of inflation in the United States over the period 1909 to 2015 has averaged 3.10% per year. You just purchased a new car for $28,000. You wonder what the cost of this same car might be 50 years from now when your son may be purchasing a similar car for his daughter (your granddaughter) so she can attend college. Also, you wonder what the value of the Model T will be 50 years in the future, that is, in the year 2065.

2. The purchase price of Manhattan Island, where much of the city of New York is concentrated, in the year 1626 was $24. After 391 years in 2017, you wonder what the value of the land might be, provided it has appreciated in value at a rate of 6% per year, every year.

3. Last week, your friend Jeremy borrowed $200 from a pawn shop operator because he was totally broke. He was to pay the operator $230 after 1 week, but missed the payment. At first, you thought this was "no big deal," but then started to realize that the interest was $30 the first week alone and would increase, compounded at the same rate until the total debt was repaid. When your friend told you he would pay off the loan in a year (provided the operator didn't come after him), you gave him the results of your analysis. He was shocked and paid the total amount immediately.

4. In 1939, two people teamed up to manufacture and market electronic test equipment. By 1957, the initial capital investment from themselves and a few friends that amounted to only $80,805.12 in 1939 had increased in value to an equivalent of $1 million. After this, the company skyrocketed to become a world leader in electronic equipment, computers, and a wide range of other products. If the net cash flow averaged $150,000 per year from 1957 to 2017 (60 years) at the same rate, these two individuals would be quite wealthy.

5. Assume that when your great-grandmother was 25 years old, she received an engagement ring from her husband-to-be. He paid $50 for the ring containing a single, high-quality diamond. When she passed away at the age of 90, the ring went to your grandmother, who kept it for 60 years and then gave it to your mother. After 30 years of keeping the ring in a safe place, she leave it to you on your 24th birthday. Today is your 48th birthday and you have just discovered the ring in a desk drawer, forgotten for all these years. If this high-grade diamond has been now appraised as a collector's grade stone, which has appreciated in value at an average rate of 4% per year, every year, since it was first purchased, you wonder what the ring might be valued at today.

Team Exercises

For each situation described. do the following using a five-person team.

(a) Determine the annual compound interest or inflation rate and discuss the differences in these rates from one situation to another.