Mathematics of Finance Presentation.pptx

This presentation is a structured communication of mathematical concepts, theories, or solutions, usually delivered orally with supporting visual aids such as slides or a whiteboard.

1. WELCOME Presented by: Md Ahsan Ullah MBA (Professional) Roll: 23230333012 Section: ‘A’ Batch: 33 rd Presented To: Professor Dr. Md. Showkat Ali Professor Faculty of Business Studies Bangladesh University of Professionals (BUP)

2. MATHEMATICS OF FINANCE

3. Mathematics of Finance Everybody uses money. Sometimes you work for your money and other times your money works for you. For example, unless you are attending college on a full scholarship, it is very likely that you and your family have either saved money or borrowed money, or both, to pay for your education. When we borrow money, we normally have to pay interest for that privilege. When we save money, for a future purchase or retirement, we are lending money to a financial institution and we expect to earn interest on our investment. We will develop the mathematics in this chapter to understand better the principles of borrowing and saving. These ideas will then be used to compare different financial opportunities and make informed decisions. Mathematics of Finance Is also known as Quantitative finance is a field of applied mathematics concerned with mathematical modeling of financial Market.

4. Functions Of Mathematical Finance Financial mathematics is the Application of Mathematical Finance. Financial Math Sometimes used in Financial Engineering, Quantitative finance.

5. Elements of Financial Matic’s Simple Interest. Compound Interest. Annuity

6. Simple Interest Simple interest is calculated only on the principal amount of a loan or deposit. Simple interest is calculated using the following formula: ​ Simple Interest= P×r×n where:   P=Principal amount, r=Annual interest rate, n=Term of loan, in years. simple interest paid or received over a certain period is a fixed percentage of the principal amount that was borrowed or lent. For example, say a student obtains a simple-interest loan to pay one year of college tuition, which costs $18,000, and the annual interest rate on the loan is 6%. The student repays the loan over three years. The amount of simple interest paid is:$3,240=$18,000×0.06×3 and the total amount paid is:$21,240=$18,000+$3,240.

7. Compound Interest As mentioned earlier, simple interest is normally used for loans or investments of a year or less. For longer periods compound interest is used. With compound interest, interest is charged (or paid) on interest as well as on principal. The formula for compound interest is:​ Compound Interest=P×(1+r) t −P where: P=Principal amount r=Annual interest rate t=Number of years interest is applied

8. Simple Vs Compound Interest

9. Annuity & its types Annuity is a series of equal payments made at equal intervals of time. The annuity formula helps in determining the values for annuity payment and annuity due based on the present value of an annuity due, effective interest rate, and several periods. Hence, the formula is based on an ordinary annuity that is calculated based on the present value of an ordinary annuity, effective interest rate, and several periods. Annuity can be classified into 2 classes: 1. Annuity certain/ ordinary annuity – payment are made at the end of each payment period. 2. Annuity due – payment are made at the beginning of each period.An annuity due is an annuity whose payment is due immediately at the beginning of each period.

10. Formula of annuity based math The formula is calculated based on two important aspects - The present Value of the Ordinary Annuity and the Present Value of the Due Annuity. Annuity = r * PVA Ordinary / [1 – (1 + r)-n] The Annuity Formulas for future value and present value is: The future value of an annuity, FV = P×((1+r)n−1) / r The present value of an annuity, PV = P×(1−(1+r)-n) / r where, P = Value of each payment r = Rate of interest per period in decimal n = Number of periods   The word present value in the annuity formula refers to the amount of money needed today to fund a series of future annuity payments.

11. Annuity Based Math Problem Problem : Dan was getting $100 for 5 years every year at an interest rate of 5%. Find the future value of this annuity at the end of 5 years? Calculate it by using the annuity formula.  

12. Solution to the problem Given: r = 0.05, 5 years = 5 yearly payments, so n = 5, and P = $100 FV = P×((1+r)n−1) / r FV = $100 × ((1+0.05)5−1) / 0.05 FV = 100 × 55.256 FV = $552.56 Therefore, the future value of annuity after the end of 5 years is $552.56.

13. Any Question ??

14. THANK YOU