There are several types of interest problems. This lesson deals with solving problems where interest is compounded and where interest is continuous.

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1 Congratulations!! You have just won $50,000! You decide to invest your money and the bank preses you with two investme options. You may either invest your $50,000 at 5% ierest, compounded mohly, for a period of ten years OR you can invest that $50,000 at 5% ierest, compounded coinuously, for ten years. You must figure out which investme option will yield a greater profit. You have already learned how to use the rules of expones to solve math problems and to solve exponeial equations. Now you will apply these concepts to solve ierest problems. There are several types of ierest problems. This lesson deals with solving problems where ierest is compounded and where ierest is coinuous. To compound ierest means adding the accumulated ierest back to the original amou in the accou. To coinuously compound ierest means adding ierest every insta The Compound Ierest Formula is A P 1 r n A represes P represes r represes t represes n represes Let s try some examples using the Compound Ierest Formula 1. Suppose Wes has $1000 that he invests in an accou that pays 3.5% ierest compounded quarterly. How much money does Wes have at the end of 5 years? How much ierest will he earn?

2 r A P1 n 2. William was to have a total of $4000 in two years so that he can put a hot tub on his deck. He finds an accou that pays 5% ierest compounded mohly. How much should William put io this accou so that he ll have $4000 at the end of two years? 3. Suppose William, from our last example, only has $3500 to invest but still was $4000 for a hot tub. He finds a bank offering 5.25% ierest compounded quarterly. How long will he have to leave his money in the accou to have $4000?

3 Ierest that is compounded coinuously seldom occurs at banks that you might deal with on a regular basis. However it is very useful for finding the maximum amou of money that can be earned at a particular ierest rate. It is a very effective way to demonstrate how powerful compounding ierest can be. You should be careful to note that for ierest compounded for any amou of time other than coinuously, there is a differe formula (the one you learned to use in the previous examples). The following applies only to ierest compounded coinuously. The formula for coinuously compounded ierest is A Pe rt A, P, r and t represe the same quaities described in the compound ierest problems above. The letter e is not a variable. It has a numeric value (approximately ) although we do not usually use the value. We simply solve the problem using the e button on the calculator. Let s try some examples using the formula for Coinuously Compounded Ierest 4. Suppose $5000 is put io an accou that pays 4% compounded coinuously. How much will be in the accou after 3 years? 5. If ierest is compounded coinuously at 4.5% for 7 years, how much will a $2000 investme be worth at the end of 7 years? 6. How long will it take $3000 to double if it is invested in an accou that pays 3% compounded coinuously?

4 Now let s go back and figure out which is the best investme option for our lottery winnings. I have re-typed the problem for you. I will collect this problem at the start of class tomorrow and grade it out of 10 pois (this will be your first grade of the 4 th quarter!). Your score will be based on the accuracy of your mathematical calculations as well as the amou of work that you show, so use the examples we did in class to help you out. Good luck! Congratulations!! You have just won $50,000! You decide to invest your money and the bank preses you with two investme options. You may either invest your $50,000 at 5% ierest, compounded mohly, for a period of ten years OR you can invest that $50,000 at 5% ierest, compounded coinuously, for ten years. Which investme option will yield a greater profit?

5 Homework: Read each problem carefully and decide which ierest formula you need to solve. Show all work! r A P1 n A Pe rt 1. Mildred plans to put her graduation money io an accou and leave it there for 4 years while she goes to college. She receives $750 in graduation money that she puts it io an accou that earns 4.25% ierest compounded semi-annually. How much will be in Mildred s accou at the end of four years? 2. ABC Bank is offering to double your money! They say that if you invest with them at 6% ierest compounded quarterly they will double your money. If you invest $1500 in the accou, how long will it take to double your money? 3. If $8000 is invested in an accou that pays 4% ierest compounded coinuously, how much is in the accou at the end of 10 years?

6 r rt A P1 A Pe n 4. How long will it take $4000 to triple if it is invested at 5% compounded coinuously? 5. Lindsay was to have a total of $3500 in two years so she can take a trip to St. Maarten. She finds an accou that pays 4% ierest compounded mohly. How much should Lindsay put io this accou so that she ll have $3500 at the end of two years? 6. Miss Young was to have a total of $30,000 in three years so that she can buy a house. She finds an accou that pays 4.25% ierest compounded mohly. How much should Miss Young put io this accou so that she ll have $30,000 at the end of three years? 7. Miss Young was to have a total of $10,000 in two years so that she can travel around the world. Suppose she finds an accou that pays 3.25% ierest compounded coinuously. How much should Miss Young put io this accou so that she ll have $10,000 at the end of two years?