TOPIC : Basics of Financial Mathematics MATHS SEMINAR - Saachi Ahuja Abstract 02 Question 03 Introduction 04 Interest 05 Types Of Interest 06 Formula's 07 Question along with explanation 08 Conclusion 09 Bibliography 10 Thank You slide STNETNOC 01 Abstract Introduction on financial Mathematics Interest Simple Interest Types Of Interest Compound Interest Formulas of compound interest Explore slide Question Interest is recorded as an expense to the borrower and income to the lender. Explain the types of interest and justify which is more profitable. Introduction Role of Financial Mathematics Financial mathematics has a large number of applications in all economic activities where there is a flow and exchange of goods and services, exchange of currency, payment of money from companies to their employees, in short, a fundamental importance in the various tasks of our daily life where an interaction between people and companies converges. It is very important that the entrant to acquire this type of knowledge understand the implications that "the variations of the value of money over time". Interest - It is the additional money besides the original money paid by the borrower to the money lender (bank, financial agency or individual) in lieu of the money used by him. Principal- The money borrowed (or the money lent) Amount- The sum of principal and the interest Thus, amount = principal + interest Rate- It is the interest paid on Rs. 100 for a specified period. Types Of Interest Simple Interest- It is the interest calculated on the original money (principal) for any given time and rate. Compound Interest - The difference between the final amount and them (original) principal is called compound interest. Interest = Amount - Principal In simple interest, interest for all years is same In Compound interest, interest for all years is different. SI is smaller than CI CI is larger than SI Interest is on principal Interest is on previous principal If Principal= Rs. ,rate = R% per annum and time = n years then, i) amount after n years (compounded monthly) ii) amount after n years (compounded annually) iii) amount after n years (compounded half-yearly) iv) amount after n years (compounded quarterly) For ₹ 10000 at 10% per annum. What will be compounded interest after 4 years ? Principal = Rs.10,000 Rate= 10 % p.a. Time= 4 years Question solved via Simple Interest To find the amount we have the formula, Interest=P*R*T/100 Simple Interest = 10,000*10*4/100 Question solved via Compound Interest To find the amount we have the formula, n Amount (A)=P(1+(r/100)) Amount=10,000 (1+(10/100)) 4 = 4,00,000/100 A=10,000 (1+1/10)) 4 A=10,000 (11/10) 4 = 4,000 A=10,000 (14,641/10,000) Amount = principal + interest Amount =14,000 SI= 4,000 A=14,641 Compound Interest = amount - principal CI= 14,641 - 10,000 CI= 4,641 Conclusion Hence, with the help of the question it is clear that Compound Interest is more profitable. Why is Compound Interest more profitable? Compound interest makes a sum of money grow at a faster rate than simple interest, because in addition to earning returns on the money you invest, you also earn returns on those returns at the end of every compounding period, which could be daily, monthly, quarterly or annually. That’s why compound interest causes your wealth grow faster. Rates Of Interest Equivalent Nominal Effective Annual Equivalent Rate is a figure which shows what the interest rate on an account would be if interest was paid for a full year and compounded. When interest is compounded more than once in a year, the given Annual rate is called nominal rate. The rate of interest actually earned is called effective rate via the example, nominal rate = 4% while effective rate is 4.06% and equivalent rate =4.06% Explore Slide Example- Consider an amount of Rs. 10,000 invested at 4% interest compounded quarterly. Now this interest of 4% is divided into four parts of 1% each. An interest of 1% as charged at the end of one quarter. Calculation for finding 1% interest at the end of each quarter Rs. 10,000 (1+ 1/100)=10,100 Rs. 10,100 (1+ 1/100)= 10,101 Rs. 10,101 (1+ 1/100)=10,102.02 Rs. 10,102.2 (1+ 1/100)=10,103.03 Hence the total would be 10,406.05 This is equivalent interest rate of 4.06% compounded annually because: Taking rate as x x/100*P=C.I x/10,000=40605 x=4.06% Applied Maths book by M.L Aggarwal 02 Techoo 03 Topper 04 Corporatefinanceinstitute.co m YHPARGOILBIB 01 THANK Have a nice day YOU
