Algebra Talk
In this week’s Algebra Talk, we will discuss the concept of compound interest along with some formulas and examples. Please start by addressing one or more of the following topics to get the discussion going:
1. Here is the formula for compound interest: Describe what the parameters A, P, r, n and t represent and give an example to show how to calculate compound interest using this formula.
2.The “Present Value” of a compound interest account is the amount of money you need to invest in the account today to accumulate A dollars. You can calculate Present Value by solving for P in the compound interest formula above. Calculate the Present Value (what you would need to invest) if you wanted to accumulate $10,000 by investing in an account for 8 years that pays 6% interest compounded monthly. If you’d like, pose some other Present Value problems for the class to solve.
3.As the number of times you compound the interest per year increases, the interest also increases. However, it will never be greater than the following formula for “continuous” compound interest: Continuously Compounding Interest Use the compound interest formula and the continuous compound interest formula to answer the following question: You just won $150,000 in the lottery and you decide to invest the money for 20 years to save for your retirement. However, you only get to choose one of the 4 options below. Which one would you pick and why?
1.A certificate of deposit paying 5.4% interest compounded annually?
2.A money market certificate paying 5.35% interest compounded semi-annually?
3.A bank account paying 5.3% interest compounded monthly?
4.A bank account paying 5.25% interest compounded continuously?
4. Explain step by step how to determine if two functions are inverses of each other. Provide a detailed example.
5.Give an example from real life where inverse functions are utilized. For ideas, look it up on the internet or find some examples in the textbook.
6.In your own words answer the following question – What is compound interest? What is the difference between compounded monthly and continuously?
