General mathematics Annuity powerpoint ppt

sample ppt

1. Future Value of Simple Annuity

2. OBJECTIVES: Define annuity payment; Differentiate simple annuity from general annuity; and, Solve problems involving future value of simple annuity.

3. Examine the term Rental payment Monthly pension Monthly payment for car loan Educational plan

4. Annuities may be classified in different ways, as follows. ACCORDING TO PAYMENT INTERVAL AND INTEREST PERIOD Simple annuity- an annuity where the payment intervals is the same as the interest period. General Annuity - an annuity where the payment intervals is not the same as the interest period.

5. ACCORDING TO TIME OF PAYMENT Ordinary annuity- an annuity which payment are made at the end of each payment interval. Contingent Annuity- an annuity which in the payment extend over an indefinite or indeterminate length of time. ACCORDING TO DURATION Annuity Certain- an annuity in which payments begin and end at definite times,

6. Example of a simple annuity – installment payment for an appliances at the end of each month with interest compounded monthly. Example of a general annuity – installment payment for an appliances at the end of each month with interest compounded annually.

7. Future Value of Simple Ordinary Annuity (F) F = R ( 1 + j) n – 1 J Where: R - is the regular payment j - is the interest rate per period, and n - is the number of payments

8. Example 1. Suppose Mrs. Remoto would like to save ₱3000 at the end of each month, for six months, in a fund that gives 9% compounded monthly. How much is the future value of her savings after 6 months? Given: R = ₱3000 term t = 6 months interest rate per annum i (12) = 0.09 number of conversions per year m = 12 interest rate per period j = = 0.0075 n = mt = (12 * 6months ( )) = 6  

9. Find: future value at the end of the term, F   F = R ( 1 + j) n – 1 j = 3,000 ( 1 + 0.0075) 6 – 1 0.0075 F = ₱18,340.89

10. Example 2. In order to save for her high school graduation, Marie decided to save ₱200 at the end of each month. If the bank pays 0.250% compounded monthly, how much will her money be at the end of 6 years?   Given: R = 200 t = 6 years i (12) = 0.250% = 0.0025 m = 12 j = = 0.0002083 n = mt = (12)(6) = 72 periods  

11. Practice: Mr. Cruz saves ₱1,500 at the end of each month in a savings account that earns 10% annual interest compounded monthly. How much will he have in the account after 3 years? A company sets aside ₱10,000 every quarter to replace its office equipment. If the fund earns 8% interest compounded quarterly, what will be the value of the fund after 5 years? 62,634.64 or 62,635 242,973.70 or 242,974

12. ACTIVITY:7 Directions: Find the future value of the following . Write your answer on a separate sheet of paper. 1. Quarterly payments of ₱2,000 for 5 years with interest rate of 8% compounded quarterly. 2. Semi-annual payments of ₱8,000 for 12 years with interest rate of 12% compounded semi-annually 3. Suppose Mrs. Remoto would like to save ₱ 3,000 every month in a fund that gives 9% compounded monthly. How much is the amount or the future value of her savings after 6 months . 4 . Peter started to deposit ₱5,000 quarterly in a fund that pays 1% compounded quarterly. How much will be in the fund after 6 years?

13. Present Value of Simple Ordinary Annuity (P)

14.   Present Value of Simple Ordinary Annuity (P) P= R [1-( 1 + j) -n ] Cash Value= DP+P j Where R is the regular payment j is the interest rate per period, and n is the number of payments

15. Example 1: Mr. Dela Cruz paid ₱200,000 as a down payment for a car. The remaining amount is to be settled by paying ₱16,200 at the end of each month for 5 years. If interest is 10.5 % compounded monthly, what is the cash price of his car? Given: R = 16,200 t = 5 years i (12) = 10.5% = 0.105 m = 12 j = = 0.00875 n = mt = (12)(5) = 60  

16. Find: P   P= R [1-( 1 + j) -n ] j = 16,200 [1-( 1 + 0.00875) -60 ] 0.00875 P = 753,702.20 or 753,702 Cash Value= DP+P = ₱200,000 + 753,702.20 = ₱953,702.20

17. Example 2. Suppose Mrs. Remoto would like to save ₱3000 at the end of each month, for six months, in a fund that gives 9% compounded monthly. How much is the present value of her savings after 6 months? Example 3. The buyer of house and lot pays ₱200,000 cash and ₱10,000 at the end of each month for 20 years. If money 9% compounded quarterly, how much is the cash value of the car? 17,536.79 or 17,537 369,497.81 or 369,498 CV = 569,497

18. Future Value of General Annuity

19.   Future Value of General Annuity F = R ( 1 + j) n – 1 j = (1+ -1 j Where: R= Regular payments n = total no. of payments j = Equivalent rate per conversion period. n = (m 1 )(t) M 1 = payment interval M 2- length of compounding period.  

20. Example 1: Mel started to deposit ₱ 1,000 monthly in a fund that pays 6% compounded quarterly. How much will be in the fund after 15 years? Given: R= ₱ 1,000; r (m 2 ) =6% or 0.06 m 1 =12 m 2 =4 t= 15 n=(12)(15) = 180

21. Solution: j= (1+ -1 j= (1+ -1 j= Finding F: F= = F= ₱ 290,082.51  

22. Example 2: Find the future value of an annuity of = ₱ 10,000.00 payable quarterly for 3 years if money is worth 12% compounded monthly. Example 3: Mrs. Santos is paying ₱11,400 monthly for 2 years compounded semi-annually at a rate of 7 % . Example 4: ABC bank pays interest at the rate of 2% compounded quarterly. How much will have in the bank at the end of 5 years if you deposit ₱ 3,000 every month?