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- Applications of Exponential and Logarithmic Functions

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Get Started Now- Lesson: 18:48
- Lesson: 26:20

In this section, we will revisit the connection between mathematics and finance, but from a different perspective. We will see how a slight variation of the Compound interest formula can help us understand some of the core concepts in Finance – Future value and Present value.

Related Concepts: Derivative of inverse trigonometric functions, Derivative of logarithmic functions

future value and present value: ${ FV = PV (1+\frac{r}{n})^{nt}}$

${FV}$: Future Value

${PV}$: Present Value

${r}$ : Annual interest rate

${t}$: total time given in**years **

${n}$ : number of times compounded in a year, if

${FV}$: Future Value

${PV}$: Present Value

${r}$ : Annual interest rate

${t}$: total time given in

${n}$ : number of times compounded in a year, if

Compound daily: |
n = 365 |

Compound monthly: |
n = 12 |

Compound quarterly: |
n = 4 |

Compound semi-annually: |
n = 2 |

Compound annually: |
n = 1 |

- 1.What is the future value of $30,000 which grows at an annual interest rate of 11%, compounded monthly, for three years?
- 2.What is the present value of $15,000 sixteen months from now if the annual discount rate is 10%, compounded quarterly?

13.

Applications of Exponential and Logarithmic Functions

13.1

Exponential growth and decay by a factor

13.2

Exponential decay: Half-life

13.3

Exponential growth and decay by percentage

13.4

Finance: Compound interest

13.5

Continuous growth and decay

13.6

Logarithmic scale: Richter scale (earthquake)

13.7

Logarithmic scale: pH scale

13.8

Logarithmic scale: dB scale

13.9

Finance: Future value and present value

13.1

Exponential growth and decay by a factor

13.2

Exponential decay: Half-life

13.3

Exponential growth and decay by percentage

13.4

Finance: Compound interest

13.5

Continuous growth and decay

13.6

Logarithmic scale: Richter scale (earthquake)

13.7

Logarithmic scale: pH scale

13.8

Logarithmic scale: dB scale

13.9

Finance: Future value and present value