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1. BUSINESS MATHEMATICS INTERESTS K ristine D. Buña

2. LESSON GOALS 1 Illustrate simple and compound interest; 2 3 Compute for the interest, maturity value, future value, and present value in simple interest and compound interest environment including payment in installment basis; and Solve problems involving simple and compound interest.

3. What is the starting point of a business?

4. Business Mathematics Business Mathematics consists of Mathematical concepts related to business. It comprises mainly profit, loss and interest. Math is the base of any business. Business Mathematics financial formulas, measurements which helps to calculate profit and loss, the interest rates, tax calculations, salary calculations, which helps to finish the business tasks effectively and efficiently. -https://byjus.com/ maths /business-mathematics/ “…mathematics not only helps to calculate but also analyze business problems and work upon them. Learning and using business mathematics enables a person to think out of the box, sharpens one’s thinking and helps in precisely formulating and structuring relationships.” https://www.educba.com/what-is-business-mathematics/

5. Thank you Insert the title of your subtitle Here Commercial organizations use mathematics in accounting, inventory management, marketing, sales forecasting, and financial analysis. It helps you know the financial formulas, fractions; measurements involved in interest calculation, hire rates, salary calculation, tax calculation etc. which help complete business tasks efficiently. Business mathematics also includes statistics and provides solution to business problems. https://www.educba.com/what-is-business-mathematics/ For those that do own a business, business math is even more important. Business math can help these individuals to be successful by providing them with a solid understanding of how to manage goods and services to make a profit. https://www.thoughtco.com/business-math-overview-231210

6. INTERESTS

7. INTEREST DEFINED The amount paid for the use of another amount of money. The money you pay on top of the amount you borrow which compensates lenders for making their money available as well as the risk they take. marketbusinessnews.com

8. BASIC TERMINOLOGIES Principal – the base in which the interest is computed. If an amount is loaned or borrowed, this amount is referred to as principal. Term – the unit of time for which the principal is loaned, or the length of time the principal is borrowed. This is expressed in years. Interest rate – the multiplier expressed as percent of the principal to be paid each term. Maturity Value – the sum of the principal and the interest that accumulates over the agreed term,

9. INTEREST SIMPLE Only the principal amount, no more no less, is considered in the computation of interest. This kind of interest is applied for transactions that usually last only for less than a year. COMPOUND It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest. Compound interest is usually applied for long term transactions.

10. SIMPLE INTEREST SIMPLE INTEREST FORMULA I is directly proportional to the principal P , interest rate r , and the term t . In symbols, I = Prt Only the principal amount, no more no less, is considered in the computation of interest. This kind of interest is applied for transactions that usually last only for less than a year.

11. MATURITY VALUE MATURITY VALUE FORMULA A = P (1 + rt ) It is the sum of the principal and the interest that accumulates over the agreed term

12. Examples: An amount of Php 1,000,000.00 is invested in a financial firm. How long will it take for the amount to reach Php 1,001,000.00 at 2% At what interest rate will it earn Php 1,000.00 in ten months?

13. TERM ORDINARY TIME It is based on a 30-day month computation. 3 months = 3 (30 days) = 90 day 11 months = 11 (30 days) = 330 days EXACT TIME Based on the exact number of inclusive dates of transaction. February 1, 2020– March 5, 2020 = 34 days November 23, 2020 – December 25, 2020 = 33 days

14. Examples: Find the exact interest and the ordinary interest given the following values: Php 30,000.00 for 100 days at 5%. Ordinary Interest/Bankers’ Rule – Makes use of 360 days as divisor to the actual number of days. Exact Interest– Makes use of 365/366 days as divisor to the actual number of days.

15. Paying on Installment Basis Rule 1 Payment received must be deducted first from the amount with interest due. The balance, the amount due after deducting the payment, is then subjected to the agreed interest and is computed from the date of last payment and the balance of the principal. INSTALLMENT PAYMENTS

16. Paying on Installment Basis Rule 2 The interest for the entire term of the principal amount is added to the maturity value. If installment payments are made, these payments plus the interest on each installment payment from the date that payment is made to the due date are subtracted from the computed value to obtain the amount due. INSTALLMENT PAYMENTS This rule is referred to as the MERCHANT RULE.

17. COMPOUND INTEREST Let P be the principal amount, r the rate, and n the number of compoundment per annum, and t for term in years. The compound amount An, at the end of the nth period is:   Compound interest is also the amount earned for one year calculated by multiplying the principal by the interest rate. They are usually used in long-term transactions.

18. Examples: Compare the maturity value of a principal value of Php 100,000.00 subjected to 6% interest in 60 days using simple interest. Compute for the maturity value if the principal amount is rolled at 6% every 60 days for one year.

19. PERIOD PER YEAR IN COMPOUND INTEREST Annual – 1 payment in one year/1 period Semiannually – 2 payments in one year/2 periods Quarterly - 4 payments in one year/4 periods Monthly - 12 payments in one year/12 periods

20. ANNUITY Annuity is another common business practice of payment. House rental, life insurance premiums, bond dividends, installment payments, and labor wages are form of annuities. Payments made annually. Forms of Annuity (depends on the mode of payment): 1. Annuity certain – an annuity with fixed dates for both the first and the last payments; 2. Contingent annuity – an annuity with indefinite dates for either the first or last payments; 3. Simple annuity – an annuity with same interest conversion dates and payment dates; 4. General annuity – an annuity where the payment dates do not coincide with the interest conversion periods; 5. Ordinary annuity – an annuity for which the payments are made at the end of the interest conversion periods; and 6. Annuity due – an annuity for which payments are made at the beginning of each interest conversion rates.

21. ORDINARY ANNUITY VS ANNUITY DUE An ordinary annuity is when a payment is made at the end of a period. An annuity due is when a payment is due at the beginning of a period. While the difference may seem meager, it can make a significant impact on your overall savings or debt payments. Which Annuity Is Best? In general, an ordinary annuity is most advantageous for consumers when they are making payments. Conversely, an annuity due is most advantageous for people when they are collecting payments. The payments made on an annuity due have a higher present value than an ordinary annuity due to inflation and the time value of money.

22. FUTURE VALUE OF ORDINARY ANNUITY The future value of an ordinary annuity for n periods at interest i per compounding period is Where p is the fixed periodic payments.  

23. Examples: Dr. Boiser deposited part of her royalty in a bank at the end of each year for 8 years. The bank paid 2.5% interest compounded annually. If she deposited Php 200,000 every year, how much did she have deposited including the interest after her 8 th deposit?

24. PRESENT VALUE OF ORDINARY ANNUITY The PRESENT value of an ordinary annuity for n periods at interest i per compounding period is Where p is the fixed periodic payments.  

25. Examples: Determine the future value and present value of an ordinary annuity for Php 300,000 investment at 2% quarterly for 5 years.

26. FUTURE VALUE OF ANNUITY DUE The future value of an annuity due for n periods at interest i per compounding period is Where p is the fixed periodic payments.  

27. Examples: Mr. Torres invested Php 10,000 in an annuity due on January 1, 2010 until December 31, 2014. The bank credits 2.2% interest compounded annually to Mr. Torres’ account. Find the future value of Mr. Torres’ Annuity.

28. PRESENT VALUE OF ANNUITY DUE The PRESENT value of an annuity due for n periods at interest i per compounding period is Where p is the fixed periodic payments.  

29. Examples: Mr. Torres signed a least contract with the owner of a commercial space worth Php 100 000 per year for five years, and made a first payment on January 1. Evaluate the present value of Mr. Torres’ 5-year lease on the same day as the first payment was made assuming a 2.2% annual compound interest rate.

30. LOAN, AMORTIZATION, AND MORTGAGE Loans are debt contract entered by two parties, organization or individual, through a note which states the principal amount, interest rate, the mode of payment and due date. Loans usually need collaterals, guarantors, and documentations. Amortization is a process of paying loan and its interest through series of regular equal payments. Mortgage is a type of secured loan that makes use of real property such a house or lot as collateral. This type of loan is usually entered into by real property buyers who do not have enough cash on hand to purchase the property.

31. AMORTIZATION AND AMORTIZATION SCHEDULE Amortization is a process of paying loan and its interest through series of regular equal payments. Formula: P = amortized loan R = periodic payment i = Interest n = period  

32. Examples: An amortized car loan of Php 1,000,000 for purchasing a brand new car is granted to Mr. Enriquez by a bank. If the loan is to be paid in 1 years at an annual interest rate of 12%, find the monthly amortization and create the amortization schedule. Payment Number Periodic Payment Interest Payment Amount Repaid Balance