1. The first mass produced automobile was the Ford Model T, initially manufactur
ID: 2613907 • Letter: 1
Question
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.Explanation / Answer
In the first situation the inflation rate is 3.1 % per year. This is the rate at which the price of the car will be increasing every year and it is based upon the average inflation from 1909 to 2015. In this scenario it is assumed that the inflation rate would continue to remain the same for the next 50 years.
In the second situation the value of the land will be increaseing @ 6% per year. Hence the inflation rate will be 6% per annum.
In the third situation we will be computing the compound interest rate using the future value formula
FV= PV*(1+r)^n
230= 200*(1+r)^1
r= Weekly interest rate = 230/200 -1 = 15%
This brings the annual rate to be 15%*52 = 780%
Hence we see that the annual compound rate is 780% in case 3 as compared to drastically smaller rates in the first 2 cases.
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