ORDINARY-ANNUITY-ABIHAYBALANECABARUBIA-2.pptx

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1. Ordinary annuity

2. Learning outcomes understand the concept of an ordinary annuity and differentiate it from other annuities. At the end of the lesson, students should be able to: calculate the future and present value of an ordinary annuity using manual calculation, table and formula. apply ordinary annuity concepts to real world financial scenarios.

3. motivational activity "PASS THE MESSAGE WITH A TWIST"

4. Ordinary annuity When the annuity payment is made at the end of each period it is known as an ordinary annuity.

5. Future value of ordinary annuity

6. manual calculation of future value

7. Manual calculation for the future value Illustration: What is the future value of an ordinary annuity of P10,000 per year, for 4 years, at 6% interest compounded annually? Because this is an ordinary annuity, the payment is made at the end of each period, in this case, years. Each interest calculation uses the formula I = PRT with R = 0.06 and T= 1 year

8. Manual calculation for the future value

9. example Find the future value of an ordinary annuity that has payments of $1,900 per year for 5 years at 15% compounded annually?

10. example Pekto decides to invest $18,000 per year for the next 2 years in an annuity, expecting it to compound at a rate of 6% quarterly.

11. future value using the table

12. As illustrated, working on annuity problems manually is quite tedious. An annuity of ten years, with payments made monthly, would require 120 calculations. As with compound interest, a table shall be used to calculate the future value of an annuity. Note: the steps for using annuity tables are similar to those used with the compound interest table. future value using the table

13. Example: Audrey Alonzo deposited P30,000 at the end of each year for 8 years in her savings account. If her bank paid 5% interest compounded annually, find the future value of Audrey’s account. Use the future value of an annuity table or Table 3. future value using the table

14. To solve for the future value, the interest rate per period and the number of compounding periods are first determined. future value using the table The interest rate per period is 5% (5% ÷ 1 period per year) and the number of compounding periods is 8 (8 years x 1 period per year).

15. Future Value = Annuity payment x Table factor Future Value = 30,000 x 9.549109 Future Value = P286,473.27 Note that the table factor in Table 3 are the values of [(1 + i)^n - 1 ] ÷ i when FV = Pmt x [(1 + i)^n - 1 ] (refer to the next discussion). Hence, the future value of the ordinary annuity is found by simply multipying the annuity payment by the table factor future value using the table OA

16. example Gracy deposits $500 into a savings account at the end of each year for 5 years. The account earns an annual interest rate of 8% Calculate the future value of the annuity using a future value of ordinary annuity table.

17. example Bilog invests $1,000 at the end of each year for 10 years into a retirement account that earns an annual interest rate of 6% Calculate the future value of the annuity using a future value of ordinary annuity table.

18. future value using the formula

19. An alternative method of solving for the future value of an ordinary annuity uses the ordinary annuity formula that requires a calculator. The formula for the future value of an ordinary annuity states FV = Pmt x (1 + i)^n - 1/ i where FV = Future value of an ordinary annuity Pmt = Annuity payment i = Interest rete per period (nominal rate ÷ periods per year n = Number of periods (years x periods per year) future value using the formula OA OA

20. Example: What is the future value of an ordinary annuity of Php 1,000 per month, for 3 years, at 12% interest compounded monthly? For this future value of an ordinary annuity problem, i = 1% (12% ÷ 12), and n = 36 periods (3 years x 12 periods per year). future value using the formula

21. example Gracy deposits $500 into a savings account at the end of each year for 5 years. The account earns an annual interest rate of 8% Calculate the future value of the annuity using a future value of ordinary annuity table.

22. example Maria deposits $200 at the end of each month into a retirement account for 20 years. If the account earns an annual interest rate of 7%, calculate the future value of the annuity.

23. Present value using the table

24. Illustration: How much must be deposited now, at 9% compounded annually, to yield an annuity payment of P50,000 at the end of each year, for 10 years? Example

25. The table factor is found by scanning across the top row of Table 4 to 9%, and down the 9% column to 10 periods. The table factor at that intersection is 6.417658. Finally, the present value of the ordinary annuity is found by multiplying the annuity payment by the table factor.

26. Present value = Annuity payment x Table factor Present value = 50,000 x 6.417658 Present value = P320,882.90 The table factors in Table 4 are the values of when (refer to next section’s discussion). Thus, the present value an ordinary annuity is found by simply multiplying the annuity payment by the table factor.

27. Find the present value of an ordinary annuity that has payments of Php 2,900 per year for 10 years at 8% compounded semi-annually? Practice

28. Present value using the formula

29. An alternative method of solving for the present value of an ordinary annuity uses the ordinary annuity formula that requires a calculator. The formula for the present value of an ordinary annuity states where PV = Present value of an ordinary annuity Pmt = Annuity payment i = Interest rete per period (nominal rate ÷ periods per year n = Number of periods (years x periods per year) OA

30. Illustration: What is the present value of an ordinary annuity of P10,000 per month, for 4 years, at 12% interest compounded monthly? For this present value of an ordinary annuity problem we shall use i = 1% (12% ÷ 12), and n = 48 periods (4 years x 12 periods per year). Example

31. Sheena have an ordinary annuity where she receives PHP 8,000 per month for 4 years, and the discount rate is 6%. Find the present value. Practice

32. Thank you! Thank you!