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Math 142 Section 1.3 Examples Example 1: We deposit $1200 into a bank account for 9 months, and withdrew $1270. What was the interest rate for the account? Example 2: Suppose $1000 is deposited in an account earning interest at 6% per year, compounded monthly. How much money will be in the account after 5 months? Math 142 Section 1.3 Examples Example 3: Suppose we invest $1200 for 3 years at 8% per year. How much do we have at the end, if we compounded a) quarterly? b) monthly? Example 4: Suppose Fred wants to take a trip to Europe at the end of his college career. If Fred needs $4,500 for this trip, how much would he need to deposit into an account paying 6.8% year compounded daily if he expects to graduate 4 years from now? How much interest did he earn? Math 142 Section 1.3 Examples Example 5: Solve for x: 9x = 274x−10 . Example 6: Suppose 4 years from now I want to buy a Death Star that costs $5000. I have an account with continuously compounded interest at an annual rate of 4%. How much money should I put into the account now in order to reach my goal? Example 7: A bank advertises a nominal rate of 6.3% compounded quarterly. What is the effective yield of an account here? Example 8: What is the effective rate of the account for my Death Star? Math 142 Section 1.3 Examples Example 9: Bank A advertises an account with a nominal rate of 7.1% compounded semiannually. Bank B has an account with a annual rate of 6.9% compounded continuously. What are the effective rates of these accounts? Which one is better for your money? Example 10: Suppose the population of a colony in 1790 is 3926 thousand people. Analysis of the population shows that it is increasing in population by 3.3% per year. Write a function P (x) for the population of the colony (in thousands). Example 11: Suppose you place $1000 under your mattress and left it there. Meanwhile, inflation continues at a rate of 3% per year. Comparatively, how much would this $1000 be worth in 5 years? (ie, what is the real purchasing power of this $1000 in terms of the present amount?)