MODULE 2 (Interest, Maturity, Future,).pptx

It contains the basic idea of Simple and compound interests. It also provides formulas that will be used in solving word problems about simple and compound interest.

1. General Mathematics Quarter 2 – Quarter 2 – Module 2: Interest, Maturity, Future, and Present Values in Simple and Compound Interests

2. After going through this module, you are expected to: compute interest, maturity value, future value, and present value in simple interest and compound interest environment (M11GM-IIa-b-1); and solve problems involving simple and compound interests (M11GM-IIb-2)

3. Interest, Maturity, Future, and Present Values in Simple Interest

4. Express the following as decimal:

5. Let us take the given example: REVIEW Example 1: Given: 𝑃 = ₱18, 500, 𝑟 = 0.03, 𝑡 = 5. Find simple interest (𝐼𝑠).

6. What if you are asked to solve the value of rate, term, principal amount and future value, how are you going to solve it?

7. Let us take the given example: LESSON PROPER Example 2: Given: 𝑃 = ₱20,000, 𝐼𝑠 = ₱4,000, 𝑡 = 4 . Find the rate (𝑟)

8. Let us take the given example: LESSON PROPER Example 2: Given: 𝑃 = ₱20,000, 𝐼𝑠 = ₱4,000, 𝑡 = 4 . Find the rate (𝑟)

9. Let us take the given example: LESSON PROPER Example 3: Given: 𝑃 = ₱40,000., 𝐼𝑠 = ₱700, 𝑟 = 7%. Find time (𝑡)

10. Let us take the given example: LESSON PROPER Example 3: Given: 𝑃 = ₱40,000, 𝐼𝑠 = ₱700, 𝑟 = 7%. Find time (𝑡)

11. Let us take the given example: LESSON PROPER Example 4: Given: 𝑃 = ₱15,000, 𝑡 = 4 months, 𝑟 = 2%. Find maturity (future) value (𝐹).

12. Let us take the given example: LESSON PROPER Example 4: Given: 𝑃 = ₱15,000, 𝑡 = 4 months, 𝑟 = 2%. Find maturity (future) value (𝐹).

13. Let us take the given example: LESSON PROPER Example 4: Given: 𝑃 = ₱15,000, 𝑡 = 4 months, 𝑟 = 2%. Find maturity (future) value (𝐹).

14. FORMULAE

15. Let us take the given example: FORMATIVE ASSESSMENT 1. If P = ₱4,500, r = 1.25% and t = 5 years, find the simple interest. 2. If P = ₱5,000 , r= 2% and t = 8 months, find the maturity value. 3. If Is = ₱625, r = 2% and t =3 years, find the present value . 4. Mary borrowed ₱ 15,000 from a bank that charges a simple interest rate of 6% per year. If the total amount of interest Mary paid at the end of the loan period was ₱ 1,800, how long (in years) did she have the loan?

16. Interest, Maturity, Future, and Present Values in Compound Interest

17. Let us take the given example: REVIEW Example 1: Given: P = ₱35,000 and Is = ₱ 4,000, find F.

18. Let us take the given example: REVIEW Example 2: Given: F = ₱50,000 and P = ₱45,000, find Is.

19. Let us take the given example: REVIEW Example 3: Given Is = ₱2,000 and F = ₱23,000, find P.

20. Interest rate - the price paid using someone’s else money. Definition of terms: Compound amount (F) – also called maturity value, it is an accrued amount obtained by adding the principal and the compound interest. Conversion period (m) – the number of periods in a year the interest will be compounded. Compound Interest - interest gained on both the principal and any interest that has been earned in the past.

21. Subsequently these are the common conversion periods in a year: annually : m = 1 semi-annually : m = 2 quarterly : m = 4 monthly : m = 12 Definition of terms:

22. Annually – it’s computation denotes once a year. Semi-annually – it’s computation occurs twice a year. Quarterly – it denotes computation four times a year interval. Monthly – it denotes computation once a month. Definition of terms:

23. Number of conversion periods (n) – the total number of times interest is computed for the entire term of the investment or loan. Definition of terms: Periodic rate ( i ) – the interest percentage per conversion cycle. Present value of F (P) – this is the principal P, that will accumulate to F if there is an interest at a periodic rate i for n conversion periods. Annual interest rate or nominal rate (r) – the stated rate of interest per year.

24. Maturity Value or Future Value (F) – sum of amount after t years that the investor collects from the debtor on the maturity date. Definition of terms: Term (t) - is a period of duration, time or occurrence, in relation to an event Compound Interest ( Ic ) is normally utilized by banks in figuring revenue for long term investments and credits, for example, investment account and time stores. Annual interest rate or nominal rate (r) – the stated rate of interest per year.

25. Problem Solving

26. Example: ₱2,000.00 was loaned for a period of 3 years with 5% interest compounded annually. What amount of money will be needed to repay the loan?

27. What if you are asked to solve the value of rate, term, principal amount and future value, how are you going to solve it?

28. Examples: 1.) Find the compound amount or maturity (future) value and compound interest earned on ₱15,000.00 for 1 year at (a) 10% compounded semi-annually and (b) 7% compounded quarterly .

29. Examples: 2.) Find the present value of ₱12,850.00 due in 3 years if the interest rate is 6% compounded monthly.

30. 3.) At what rate of interest compounded semi-annually will ₱14,300.00 accumulate to ₱17,000.00 in 2 years and 6 months?

31. 4.) How many years will it take for ₱13,000.00 to become ₱20,000.00 at 12.5% compounded annually ?

32. Assessment 1. Joseph borrows ₱50,000.00 and promise to pay the principal and interest at 12% compounded monthly. How much must he repay after 6 years? 2. A loan ₱125,000.00 at 8% compounded quarterly was paid back with an amount of ₱176,000.00 at the end of the period. For how long was the money borrowed?