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sIMPLE AND COMPOUND SIMPLE AND COMPOUND PPT
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- 3. Mathematics of financeis a branch of applied mathematics that deals with financial concepts and problems using mathematical tools. It combines elements of calculus, statistics, and probability to analyze financial data and model financial instruments.
- 4. Part I:SIMPLE ANDCOMPOUND INTEREST Part II:CREDIT CARDS AND CONSUMER LOANS Part III:STOCK,BONDS AND MUTUAL FUNDS TYPES OF MATHIMATICS OF FINANCE
- 5. SIMPLE INTEREST --simple interestis the interest charge on borrowing that's calculated using an original principal amount only.And an interest rate that never changes. --This is the interest in which only the original principal bears interest for the entire of term of the loan.
- 6. DEBTOR OR MARKER-- The person who barrows money for any purpose LENDER -- The person or institution which loans the money INTEREST --The payment for the use of borrowed money PRINCIPAL --The capital or sum of money invested
- 7. RATE OR INTEREST--The fractional part of the principal that is paid on the loan TIME OR TERM -- The number of units of the time for which the money is borrowed and for which interest is calculated FINAL AMOUNT OR MATURITY VALUE --The sum of the principal and interest which is accumulated at a certain time PRESENT VALUE -- the amount received by the borrower
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- 9. To buy anew smartphone for hes son's online class,Sarah went to her friend Angie and barrowed 6,000 pesos at 10% for year since Sarah has to pay 6,500 pesos after a Year she.plans to sell mango as an extra source of income.
- 10. SIMPLE INTEREST Formula: I= P * r * t where: I - simple interest P - principal amount r - rate or percent of interest t - units of time (usually in years)
- 11. Solution: I=P*r*t I=6,000 x 10%x 1 I=600 pesos that means Sarah has to pay Php 600 in interest on the loan.
- 12. SIMPLE INTEREST F=P+ IF=P+Prt F=P(1+rt)
- 13. SIMPLE INTEREST the termor time may be stated in any of the following ways: a.when the time is expressed in number of years (s),the formula will be: b.when the time is expressed in number of months (s): I= P * r * number of months 12 I= P * r * number of years
- 14. Ex. Carla is investing300.00 pesos for years,The interest rate is 5.4% how much interest will Carla earn after 3years? I=Prt =(300,000)(5.4%)(3) I=48,600.00 pesos
- 15. let's try this: Howmuch interest would you earn after 1year if you put 6,000 in an account with an interest rate of 6%?
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- 17. Ex. Find the interestand amount on 41,000 pesos at 4¼% simple interest for 9 months. I=prt =(41,000)(4¼%)(9/12) I=130,687.7 F=P+I F=41,000+130,687.7 F=171,687.7 pesos
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- 19. compound interest isthe interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.it allows your investment to grow at a faster rate compared to simple interest,which is calculated only on the principal amount
- 20. FORMULA A = P(1+ - ) r n nt Where: A= final amount P= initial principal balance r= interest rate n= number of times interest applied per time period t= is the number of years the money is invested or borrowed for.
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- 22. Example 1 Jerald deposited10,000 in a savings account for ₱ five (5) years at 10% compounded semi-annually.How much will he have in his account at the end of five (5) years?How much will be the interest of his investment? Given P=10,000 r =10% or 0.10 n= 2 t=5 solution A = p(1+ - ) r n nt =10,000(1+ -- ) 0.10 2 (2).(5) = 10,000(1.05) (10) = 10,000(1.628894627774 =16,288.94
- 23. Example 2 How muchinterest is earned after 15 years by 25,000 at 8% interest compounded ₱ quarterly? Given P=25,000 r=8% or 0.08 t=15 n= 4 Solution A = P (1+ - ) r n nt = 25,000 (1+ - 0.08 4 ) (4)(15) = 25,000(1.02) (60) = 25,000(3.2810307883654 = 82,025.76 =82,025.76 - 25,000 =57,025.76
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- 26. CREDIT CARD a plasticcard that contains information and authorizes the person who's name appears on it to charges purchases or services to his her account for which he/she I will be later billed.
- 27. CREDIT CARD A finance chargesis an amount paid in excess of the cash price it is the cost of the consumer for the use of credit.most credit card company issue monthly bills. F= prt Calendar January 31 February 28 March 31 April. 30 May. 31 June. 30 July 31 August 31 September 30 October. 31 November 30 December 31
- 28. FORMULA Average Daily Balance Sumof the total amounts owed each day of the month number of days in billing period =
- 29. EXAMPLE Suppose an unpaidbill for 15,550 had a due date of august 9. A ₱ purchase of 2,800 was mode on august 18,and 1,200 was charges ₱ ₱ on august 28. A payment of 5,000 was made on August 20. The next ₱ billing date is September 9.The interest rate on the average daily balance is 3.5% per month.find the finance charge on September 9 bill. Date August 9-17 August 18-19 August 20-24 August 28-sept 8 Payment of purchase 2,800 5,000 1,200 Balance each day 15,550 18,350 13,350 14,550 Number of days until balance changes 9 2 8 12 unpaid balance times number of days 139,950 36,700 106,800 174,600 ₱458,050
- 30. ADB = 458,050= 14,775.81 31 F= 14,775.81 (0.035) (1)
- 31. EXAMPLE: Ex. A creditcard account had a $3,536 balance on February 8.A purchase of $2,448 was made on February 12, and a payment of $1,000 was mad on February 28. Find the finance charge with an interest rate of 3% ,and the average daily balance in the billing date is March 9. Date Feb 8-11 Feb 12-27 Feb 28- march 8 payment of purchase ₱2,448 ₱1,000 balance each day ₱3,536 5,984 4,984 numbers of days until balance changes 4 16 9 unpaid balance times number of days 14,144 95,744 44,856 ₱ 154,744
- 32. ADB = 154,744= 5526.5 F= PST = 5526.57(0.03)(1) = 16.5771 28
- 33. CONSUMER LOANS - ithas a fixed date for monthly repayments,where many people know-how to control their finances.
- 34. loan agreement havemany forms and with varied terms,ranging from simple promissory notes between friends and family members to more complex loans like mortgage,auto,payday and student loans.
- 35. TYPES OF LOANS 1.student loans 2. mortgages 3. car loans 4. personal loans 5. payday 6. borrowing from retirement and life insurances 7. consolidated loans 8. borrowing from friends and family 9. cash advances
- 36. Types of loans 1.STUDENT LOANS
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- 38. Types of loans 3.AUTO/CAR
- 39. Types of loans 4.PERSONAL LOANS
- 40. Types of loans 5.PAYDAY LOANS
- 41. Types of loans 6.BORROWING FROM RETIREMENT & LIFE INSURANCE
- 42. Types of loans 7.CONSOLIDATED LOANS
- 43. Types of loans 8.BORROWING FROM FRIENDS AND FAMILY
- 44. Types of loans 9.CASH ADVANCES
- 45. THE NATURE OFSTOCK AND BONDS STOCK -A stock is ownership in a company. BONDS- sold on the market - Fixed income securities cost of bond = Face value × percent of face interest of bond = Face value × annual rate
- 46. EXAMPLE 1: Findthe cost of 4000 worth of ₱ fixed income,which is sold for 80% .How much interest will they pay you if the annual Interest is 4%? Face value = 4000 percent = 80% or 0.80 cost of bond = Face value × percent = 4000 × 0.80 = 3200 Interest = 4000 (0.04) = 160
- 47. MUTUAL FUND • Acollection of stocks and/or bonds • Each investor owns shares, which represents a portion of the holdings of the fund Note: Mutual fund can be computed using Net Assest Value . NAV = A - L - ______ N where A = asset value = stocks + bonds L= liabilities N = number of shares outstanding Shares to purchase = INVESTMENT ______________ NAV
- 48. EXAMPLE 2: Amutual fund has 400 million worth of ₱ stocks and 10 million worth of bonds.The total funds ₱ liabilities are worth 3 million.There are 30 million ₱ ₱ shares outstanding.rylee Invest 50,000.00 to this fund. ₱ 1. Calculate the NAV 2. How many shares can be purchase? A= c + b = 400M + 10M = 410M NAV = A - L _____ N = 410M - 3M ___________ 30M = 13.57 shares to purchase = investment ___________ NAV = 50,000 _______ 13.57 = 3684
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- 51. WHAT IS STOCK? - Astock (also known as equity)is a security that represents the ownership of a fraction of a corporation. - This entitles the owner of the stock to a proportions assets and profits equal to how much stock they own
- 52. WHAT IS STOCK? -A stock or equity is a share of individual companies or persons.untis of stock are called "shares" - stock market is a place where stock are bought and sold -The Philippines stock exchange (PSE) is the corporation that governs our local stock markets
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- 54. PREFERRED STOCK Is aclass of corporate stock in which the investor has preferential rights over the common shareholders to dividends and a company assets are categories. NON - PARTICIPATING STOCKS Nonparticipating stocks means that shareholders received only fixed dividend.
- 55. PARTICIPATING STOCKS Participating stockmeans that shareholders may receive additional dividends if the company performs well. COMMON STOCK Is a class of corporate stock in which the investor has voting rights and shares directly in the success or failure of the business.
- 56. TYPES OF PREFERREDSTOCK
- 57. COMULATIVE PREFERRED STOCK isa type of preferred stock that receives a dividend each year. means the stock may be exchanged or a specified number of common shares in the future.
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- 59. WHAT IS MUTUALFUNDS? A mutual fund is a company that pools money from many investment and invest the money is securities such as stocka,bonds,and short - term debt.The combined holdings of the mutual fund are known as it's portfolio.investors buy shares in mutual funds.
- 60. TYPES OF MUTUAL FUNDS MONEYMARKET FUNDS A money market fund is a type of mutual fund that has relatively low risk compared to other mutual funds and most other investment and historically has had lower returns,these funds invest in short - term debt securities such as treasury bills and commercial papers, with the objective of providing liquidity and low -risk investment options.
- 61. BOND FUNDS A bondfund is a mutual fund or an exchange -traded fund (ETF) that buys and sells debt instruments like government and corporate monthly income for investors.for an investor,a bond fund is an alternative to buying individuals bonds. INCOME FUNDS An income fund is mutual fund or a ULIP (unit-linked investment plan) or any other type of investment that aims at generating an income stream for investors by investing in fixed income securities like government securities or gsecs/gilts,bonds,debentures,fixed deposit
- 62. INTERNATIONAL FUNDS These fundsinvest in stocks and bonds of companies outside the investors home country, with the objective of diversifying the portfolio and generating higher returns. SECTOR FUNDS These funds invest in stocks of companies belonging to a particular sector,such as technology, healthcare,or energy, with the objective of generating high returns from that sector.
- 63. INDEX FUNDS Index fundsthese funds invest in the stocks of a specific index,such as the 5&P 500 or the BSE sensex, with the objective of replicating the performance of the index. DEPT FUNDS These funds invest in fixed income securities such as bonds, treasury bills,and other debt instruments, with the objective of generating regular income.
- 64. EQUITY FUNDS These fundsinvest in stocks of various companies with the objective of generating long -term capital appreciation. BALANCE FUNDS These funds invest in a mix of equuty and debt securities, with the objective of generating both capital appreciation and regular income.
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