Mathematics of Finance

Compound Interest, Annuities, and Amortization of Loans
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  • Lectures 22
  • Length 2.5 hours
  • Skill Level Beginner Level
  • Languages English
  • Includes Lifetime access
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About This Course

Published 5/2015 English

Course Description

Learn the basics of the mathematics behind finance. In this course you will learn about compound interest, annuities, and amortization of loans. For more details check out all the lecture titles and descriptions!

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Curriculum

Section 1: Compound Interest
07:18

In this video you will be introduced to common terms used in the theory of interest such as present value, future value, annual interest rates, and periodic interest rates. You will also learn the main compound interest formula.

07:36

After watching this video you will have a better understanding of the compound interest formula and the different terms that appear in it. You will know how to calculate the future value of an investment and the interest earned.

05:22

After watching this video you will know what an effective rate is and how to calculate it. You will be able to use the effective rate to compare two different investments (with different rates and compound frequencies), to find out which investment is the better choice.

03:51

After watching this video you will be able to figure out how much to invest so that it grows to a specific value in the future for a given interest rate.

06:33

After watching this video you will know how to find the interest rate which will grow your investment to a specific future value over a specific length of time.

07:21

After watching this video you will be able to find the length of time it takes for some initial principal to grow to a specific future value under a given interest rate.

Section 2: Interest Compounded Continuously
07:54

After watching this video you will understand what it means for interest to be compounded continuously. You will also learn about a famous mathematical constant called Euler's number and will find out its relationship to compound interest.

04:14

After watching this video you will understand the main formula for interest compounded continuously. The formula is derived in this video.

05:35

After watching this video you will be able to calculate the effective rate for interest compounded continuously. You will be able to use it to compare investments.

04:46

After watching this video you will know how to solve for time in the formula for interest compounded continuously. You will also learn to solve for the nominal rate. Therefore you will be able to calculate the length of time for an investment to grow to a specific amount when interest is compounded continuously. You will also know what rate is required so that an investment grows to a specific amount in a fixed amount of time when interest is compounded continuously.

Section 3: Review
06:28

In this video we quickly review the main concepts and formulas in the previous videos.

Section 4: Annuities
09:34

After watching this video you will know what an annuity is. We talk about the difference between an ordinary annuity and an annuity due. You will also understand what the present value and future value of an annuity are. We do not introduce any new formulas in this video.

03:57

In this video we define what a geometric series is and find a formula for its sum. This formula is necessary for finding the present value and future value formulas for annuities. This formula only gets used in the next two videos which are derivation videos. If you want you can skip this video as well as the next two if you are not as interested in the math behind the formulas. It will give you a better understanding of the material though.

06:56

In this video we derive the future value formula for an ordinary annuity. If you want to skip this video and just see how we use the formula later then that is fine.

05:33

In this video we derive the present value formula for an ordinary annuity. If you want to skip this video and just see how we use the formula later then that is fine.

07:44

After watching this video you will know what the present value and future value formulas are for an ordinary annuity. You will also know some common finance notation which gets used when using these formulas.

07:08

After watching this video you will be able to calculate the future value of an ordinary annuity.

04:00

After watching this video you will be able to calculate the present value of an ordinary annuity. This video is a continuation of the example from the previous video.

06:06

After watching this video you will know the present value and future value formulas for annuities due. In this video we only derive the formulas so feel free to skip to the next video where we show how to use them.

08:34

After watching this video you will be able to calculate the present value and future value for annuities due.

Section 5: Amortization of Loans
12:55

After watching this video you will be able to calculate different quantities related to the amortization of loans. You will be able to calculate the periodic payment, the outstanding principal, the interest in a specific payment, the principal contained in a specific payment, and the total interest paid.

07:00

After watching this video you will know what it means to amortize a loan. You will also learn five different amortization formulas. These formulas will be used in an example in the next video.

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Instructor Biography

Chris Levy, PhD Applied Mathematics

My name is Chris Levy and I have a PhD in applied mathematics from Dalhousie University. I live in Halifax, Nova Scotia, Canada.

I am a researcher, university instructor, and a budding data scientist. I have experience teaching university courses such as calculus, differential equations, and math for commerce. I have taught courses to 35 students, 70 students, and even 300 students.

I also have experience tutoring hundreds of students in mathematics. I know how to explain concepts clearly and concisely. I have been a very successful student and instructor. I know what it takes to succeed.

I enjoy hanging out with my wife and three kids, playing guitar, playing sports, and learning.

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