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# SIMPLE-and-COMPOUND-INTEREST.pptx

GENERAL MATHEMATICS

GENERAL MATHEMATICS

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### SIMPLE-and-COMPOUND-INTEREST.pptx

1. 1. SIMPLE INTEREST
2. 2. NAME ME ACTIVITY •It is interest that is computed on the principal. The interest remains constant throughout the term. •A person (or institution) who invests the money or makes the funds available •A person (or institution) who owes the money or avails of the funds from the lender •It is the date on which money is received by the borrower
3. 3. •It is date on which the money borrowed or loan is to be completely repaid. •It is the amount of time in years the money is borrowed or invested; length of time between the origin and maturity dates •It is the amount of money borrowed or invested on the origin date
4. 4. •It is the annual rate, usually in percent, charged by the lender, or rate of increase of the investment •It is the amount paid or earned for the use of money •It is the amount after t years that the lender receives from the borrower on the maturity date
5. 5. SIMPLE INTEREST FORMULA I = Prt •where: Is= Simple Interest P= Principal or amount invested or borrowed r= simple interest rate t= term of time in years
6. 6. The formula can be manipulated to obtain the following relationships: •The formula for finding the principal amount 𝑃= Is 𝑟𝑡 •The formula for finding the rate r = Is 𝑃𝑡
7. 7. • The formula for finding the time t = Is 𝑃𝑟 • To find the maturity (future) value, you can use either of the following: 𝐹=𝑃 (1+𝑟𝑡) or 𝐹=𝑃 + 𝐼𝑠 where: F = maturity (future) value Is = simple interest P = principal or the amount invested or borrowed or present value r = simple interest rate t = time or term in years
8. 8. Ordinary and Exact Simple Interest •In ordinary simple interest, the interest is computed on the basis of one banker’s year. 1 banker’s year= 12 months = 300 days •In exact simple interest, the interest is based on the exact number of days of the year, where there are 365 days for an ordinary year and 366 days for leap years.
9. 9. LET’S PRACTICE 1. A working student at one of the biggest fast- food restaurants in Lucena City wants to save for the upcoming school year. He wants to deposit his money to a Filipino owned bank so that even in a simple way he can help his fellow Filipino. Supposed his monthly salary is ₱10,000.00, and it was deposited to an account that earns a simple interest of 2.75% per annum. Find the simple interest after 6 months, one year, and 18 months.
10. 10. 2. Due to COVID-19 pandemic Miss Dada a female resident of Brgy. May Pagkakaisa somewhere in Quezon Province thinks of a business that can provide for her needs as well as the need of her neighbors so she can be of help even in this trying time. Having no money at hand she decided to borrow from a bank as the start-up capital of ₱50,000.00 at 7% simple interest rate payable within 5 years. Compute for the interest yield.
11. 11. 3. Find the interest on 6800.00 for 3 years at 11% simple interest. 4. What is the principal amount if the amount of interest at the end of 2 1 2 year is P4,500 for a simple interest of 6% per annum? 5. If P16,000 earns P480 in 9 months, what is annual rate of interest?
12. 12. 6. Given: 𝑃=₱18,500, 𝑟=0.03, 𝑡=5. Find simple interest (𝐼𝑠) 7. Given: 𝑃=₱20,000, 𝐼𝑠=₱4,000, 𝑡=4 . Find the rate (𝑟) 8. Given: 𝑃=₱40,000., 𝐼𝑠= ₱700, 𝑟=7%. Find time (𝑡). 9. Given: 𝑃=₱15,000, 𝑡= 4 months, 𝑟=2%. Find maturity (future) value (𝐹). 10. If P = ₱5,000, r = 2% and t = 8 mos., find the maturity value.
13. 13. COMPOUND INTEREST
14. 14. Compound interest (𝑰𝒄) is the interest computed on the principal and also on the accumulated past interest, so compound interest is a way to earn money because you don’t just earn using your original money, but also the interest you earned. 𝑰𝒄 = F – P
15. 15. •If you are a debtor compound interest is not good for you. Better yet pay your debt in full the soonest possible so that the burden of interest will not be on your shoulder. •Conversely, if you are an investor, compound interest is your best buddy and it is better to invest in a long period of time for you to have a greater return of your investment through interest earned.
16. 16. •To demonstrate this, consider an investment of P1000 to earn 10% per year for three years. The following diagram shows how the money grows. P1000 P1100 P1210 P1331
17. 17. EXAMPLE 1. Due to COVID-19 pandemic Miss Dada a female resident of Barangay May Pagkakaisa somewhere in Quezon Province thinks of a business that can provide for her needs as well as the need of her neighbors so she can be of help even in this trying time. Having no money at hand she decided to borrow from a bank as the start-up capital of ₱50,000.00 at 7% interest rate compounded annually and payable within 5 years. Compute for the interest yield.
18. 18. EXAMPLE
19. 19. EXAMPLE
20. 20. EXAMPLE
21. 21. 2. Assuming that your father asks you about investment and wants to know the interest that will be earned if he will invest ₱500,000.00 in a certain bank that offers an annual compounding interest of 8% for 5 years.
22. 22. •Notice that the formula to find the future value in a compound interest is given by F = P(1+r)t where: 𝐹 = future value 𝑃 = principal amount 𝑟 = compound interest rate 𝑡 = time or time in years. • Also, to find the compound interest just deduct the principal (P) from the computed future value (F).
23. 23. 3. Given that F = ₱60,000 and P = ₱45,000 how much is the compound interest?
24. 24. 4. Accumulate P5,000 for 10 years at 8% compounded annually.
25. 25. QUIZ #2 Direction. Provide the following answers. A. Supposed that a local farmer wants to borrow money from Landbank of the Philippines to start the organic farming in his one (1) hectare of agricultural land. The farmer needs ₱150,000.00 as start-up capital. The bank offers him 10% interest rate compounded annually. Compute for the total amount to be paid every year for 5 years. Show your answer in tabular form.
26. 26. P150,000 10% P181,500 10% 10% 10% 10% P16,500 P199,650 Complete the table below and provide solutions for each of the unknown. P219,615 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
27. 27. 16. 17. 18. 19. 3 years 20. B. Complete the table below and provide solutions for each of the unknown.
28. 28. Example 1: Given: P= ₱18,500, r = 3% and compounded annually for 3 years, find the maturity value (F) and the compound interest (Ic ). Example 2: Given F = ₱15,000, r = 2% compounded annually for 4 years, find the present value (P).
29. 29. Compounding More Than Once a Year In the examples above the interest are compounded annually, however, there are cases that interest is compounded more than once a year so in this case additional terms must be clarified such as:
30. 30. •The interval of time between successive conversions of interest into principal is called the interest period or conversion period •It is usually either three months, six months or one year, in which cases interest is said to be compounded quarterly, semiannually, or annually respectively. The total amount due at any time is called the compound amount. •
31. 31. Frequency of Conversion(m) – number of conversion period in one year Conversion or interest period – time between successive conversions of interest Total number of conversion periods(n) n = mt = (frequency of conversion) x (time in years) Nominal rate (𝑖(𝑚) ) – annual rate of interest Rate(j) of interest for each conversion period j = 𝑖(𝑚) 𝑚 = 𝑎𝑛𝑛𝑢𝑎𝑙 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑜𝑓 𝑐𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛
32. 32. Example 3. Given 𝑃 = ₱50,000.00, 𝑖4 = 0.03, 𝑚 = 4, 𝑡 = 4, find F and Ic . Example 4. Given = ₱45,000.00, 𝑖2 = 0.02, 𝑚 = 2, 𝑡 = 4, find Ic .
33. 33. 5. Find the compound interest and maturity value if P = ₱43,000, with a rate of 5% is compounded semi-annually for 6 years. 6. Find the compound interest and present value if F = ₱105,000 with a rate of 2.5% is compounded quarterly for 3 years.