{"id":252,"date":"2023-06-21T13:22:48","date_gmt":"2023-06-21T13:22:48","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/why-it-matters-exponential-and-logarithmic-functions\/"},"modified":"2024-01-09T16:35:30","modified_gmt":"2024-01-09T16:35:30","slug":"why-it-matters-exponential-and-logarithmic-functions","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/why-it-matters-exponential-and-logarithmic-functions\/","title":{"raw":"Chapter 5A. Exponential and Logarithmic Functions","rendered":"Chapter 5A. Exponential and Logarithmic Functions"},"content":{"raw":"

Why It Matters: Exponential and Logarithmic Functions<\/h2>\r\nMany sources credit Albert Einstein as saying, \u201cCompound interest is the eighth wonder of the world. He who understands it, earns it ... he who doesn't ... pays it.\u201d You probably already know this if you have ever invested in an account or taken out a loan. Interest is the amount added to the balance. The beauty, in the case of investing, is that once interest is earned, it also earns interest. This idea of interest earning interest is known as compound interest. (It isn\u2019t quite as beautiful on money you owe.)\r\n\r\nInterest can be compounded over different time intervals. \u00a0It might be compounded annually (once per year), or more often, such as semi-annually (twice per year), quarterly (four times per year), monthly (12 times per year), weekly (52 times per year), or daily (365 times per year). There is also one more option\u2014compounded continuously\u2014which is the theoretical concept of adding interest in infinitesimally small increments. Although not actually possible, it provides the limit of compounding and is therefore a useful quantity in economics.\r\n\r\n\"\"\r\n\r\nSuppose you inherit $10,000. You decide to invest in in an account paying 3% interest compounded continuously. What will the balance be in 5 years, 10 years, or even 50 years? You\u2019ll want to know, especially for retirement planning.\r\n\r\nIn this module, you will learn about the function you can evaluate to answer these questions. You will also discover how to make changes to the variables involved, such as time or initial investment, to alter your results.","rendered":"

Why It Matters: Exponential and Logarithmic Functions<\/h2>\n

Many sources credit Albert Einstein as saying, \u201cCompound interest is the eighth wonder of the world. He who understands it, earns it … he who doesn’t … pays it.\u201d You probably already know this if you have ever invested in an account or taken out a loan. Interest is the amount added to the balance. The beauty, in the case of investing, is that once interest is earned, it also earns interest. This idea of interest earning interest is known as compound interest. (It isn\u2019t quite as beautiful on money you owe.)<\/p>\n

Interest can be compounded over different time intervals. \u00a0It might be compounded annually (once per year), or more often, such as semi-annually (twice per year), quarterly (four times per year), monthly (12 times per year), weekly (52 times per year), or daily (365 times per year). There is also one more option\u2014compounded continuously\u2014which is the theoretical concept of adding interest in infinitesimally small increments. Although not actually possible, it provides the limit of compounding and is therefore a useful quantity in economics.<\/p>\n

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Suppose you inherit $10,000. You decide to invest in in an account paying 3% interest compounded continuously. What will the balance be in 5 years, 10 years, or even 50 years? You\u2019ll want to know, especially for retirement planning.<\/p>\n

In this module, you will learn about the function you can evaluate to answer these questions. You will also discover how to make changes to the variables involved, such as time or initial investment, to alter your results.<\/p>\n\n\t\t\t

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Candela Citations<\/h3>\n\t\t\t\t\t
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CC licensed content, Original<\/div>