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RealLife Math Phần 4

Tham khảo tài liệu 'reallife math phần 4', ngoại ngữ, anh ngữ phổ thông phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Exponents money in your account after n quarters P is your principal the money you start off with in this case 100 and r is the quarterly interest rate 1.5 in this case . Since time n is in the exponent this is an exponential function. Putting in our numbers for P r and n we find that S n 100 1 .015 n 100 X 1.015n. For the end of the second quarter n 2 this gives the result already calculated S 2 103.02. This equation for S n should look familiar. It has the same form as the equation for a growing population R t R0bt with R0 set equal to 100 and b set equal to 1.015. If 100 is put in the bank when you re 14 then by the time you re 18 four years or 16 quarters later it will have grown exponentially to 100 X 1.01516 126.90 rounded up . If you had invested 1 000 it will have grown to 1 268.99. That s lovely but meanwhile there s inflation which is exponentially making money worth less over time. Inflation occurs when the value of money goes down so that a dollar buys less. As long as we all get paid more dollars for our labor higher wages we can afford the higher prices so inflation is not necessarily harmful. Inflation is approximately exponential. For the decade from 1992 to 2003 for example inflation was usually around 2.5 per year. This is lower than the 6 per year interest rate we ve assumed for your invested money so your 100 of principal will actually gain buying power against 2.5 annual inflation but not as quickly as the raw dollar figures seem to show after four years you ll have 26 more dollars than you started with 126.90 versus 100 but prices will be 10.4 higher i.e. something that cost 100 when you were 14 will cost about 110 when you are 18 . Furthermore 6 is a rather high rate for a savings account during the last decade or so interest rates for savings accounts have actually tended to be lower than inflation so that people who keep their money in interestbearing savings accounts have actually been losing money This is one reason why many people invest