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Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 61. A major complaint of professors teaching calculus is that students don't have the appropriate background to work through the calculus course successfully. This text is targeted directly at this underprepared audience. This is a single-variable (2-semester) calculus text that incorporates a conceptual re-introduction to key precalculus ideas throughout the exposition as appropriate. This is the ideal resource for those schools dealing with poorly prepared students or for schools introducing a slower paced, integrated precalculus/calculus course | 18.5 Applications of Geometric Sums and Series 581 EXAMPLE 18.12 SOLUTION The sum of money in the account is 200 1.05 3 200 1.05 2 200 1.05 200 862.03. Marietta cannot yet take her trip. On January 1 2004 before Marietta makes a fifth payment the first payment has grown to 200 1.05 4 the second payment has grown to 200 1.05 3 the third payment has grown to 200 1.05 2 the fourth payment has grown to 200 1.05 . The sum of money in the account is 200 1.05 4 200 1.05 3 200 1.05 2 200 1.05 . This is just the previous sum multiplied by 1.05 because the money has collected interest for another year . 862.03 1.05 905.12. Marietta can be on her way with 5.12 in her pocket as a slush fund. Mass Millions is a state-run lottery encouraging residents to support the state s public services by dangling the elusive prize of 1 million for the price of a winning lottery ticket. Instead of a million dollars however the winner actually receives 20 annual payments of 50 000. While this is a hefty sum is this really a prize of 1 million If you received 1 million today and put it into a bank account paying interest at a rate of 5 per year just by taking the interest at the end of each year you could pay yourself 50 000 per year starting one year hence and continuing on forever. The original million would stay in the bank generating interest. The 20 payments of 50 000 spread out over 20 years is not really the same as winning 1 million paid up front now. Assume the first payment is made to you today and the 20th payment 19 years later. Let s compute the up-front value of the prize money of 20 annual payments of 50 000. The first payment of 50 000 received today is certainly worth 50 000 today. But how much is the second payment of 50 000 worth to you right now How much is the 20th payment worth right now Let s rephrase the question. Let s suppose that at the moment you win the prize the state creates a bank account especially for you. The state puts a certain amount of money P into the .
