General Annuity PPT -General Mathematics

Its nice

1. GENERAL ANNUITY

2. GENERAL ANNUITY – an annuity where the length of the payment interval is not the same as the length of the interest compounding period. GENERAL ORDINARY ANNUITY – a general annuity in which the periodic payment is made at the end of the payment interval.

3. Examples of general annuity: Monthly installment payment of a car, lot, or house with an interest rate that is compounded monthly. Paying a debt semi-annually when the interest is compounded monthly.

4. FUTURE AND PRESENT VALUE OF A GENERAL ORDINARY ANNUITY The future value F of General Ordinary Annuity   The present value F of General Ordinary Annuity   Where: R is the regular payment j is the equivalent interest rate per payment interval converted from the interest rate per period; and n is the number of payments

5. Note: The formulas for F and P are same as those in simple annuity. The extra step occurs in finding j: the given interest rate per period must be converted to an equivalent rate per payment interval.

6. Example 1: Cris started to deposit P1,000 monthly in a fund that pays 6% compounded quarterly. How much will be in the fund after 15 years? Given: R = 1,000 t=15 = 6 % = 12 =   Find: F Solution: Step 1: Convert 6% compounded quarterly to its equivalent interest rate for monthly payment interval.                  

7. Step 2: Apply the formula in finding the future value of an ordinary annuity using the computed equivalent rate. Thus, the interest rate per monthly payment interval is 0.00498 or 0.498%.               Thus, Cris will have P290,224.90 in the fund after 15 years.

8. Example 2: A teacher saves P5,000 every 6 months in a bank that pays 0.25% compounded monthly. How much will be her savings after 10 years? Find: F Solution: Step 1: Convert 0.25% compounded monthly to its equivalent interest rate for each semi-annual payment interval.                   Given: R = 5 ,000 t=10 = 0.25% = 2 =  

9. Step 2: Apply the formula in finding the future value of an ordinary annuity using the computed equivalent rate. Thus, the interest rate per semi-annual payment interval is 0.00126 or 0.126%.               Thus, a teacher will have P101,190.50 in the fund after 10 years.

10. Example 3 : Ken borrowed an amount of money from Kat. He agrees to pay the principal plus interest by paying P38,973.76 each year for 3 years. How much money did he borrow if interest is 8% compounded quarterly? Find: P Solution: Step 1: Convert 8 % compounded quarterly to its equivalent interest rate for each payment interval.                   Given: R = 38,973.76 t=3 = 8 % = 1 =  

11. Step 2: Apply the formula in finding the present value of an ordinary annuity using the computed equivalent rate. Thus, the interest rate per payment interval is 0.08243 or 8.243%.               Hence, Ken borrowed P100,003.94 from Kat.

12. Example 4: Mrs. Remoto would like to buy a television (TV) set payable for 6 months starting at the end of the month. How much is the cost of the TV set if her monthly payment is P3,000 and interest is 9% compounded semi-annually? Find: P Solution: Step 1: Convert 9% compounded semi-annually to its equivalent interest rate for each monthly payment interval.                   Given: R = 3,000 t=0.5 = 9% = 12 =  

13. Step 2: Apply the formula in finding the present value of an ordinary annuity using the computed equivalent rate. Thus, the interest rate per month payment interval is 0.00736 or 0.736%.               Thus, the cost of the TV set is P17,551.62

14. ANOTHER EXAMPLES: ABC Bank pays interest at the rate of 2% compounded quarterly. How much will Ken have in the bank at the end of 5 years if he deposits P3,000 every month? A sala set is for sale at P16,000 in cash or on monthly installment of P2,950 for 6 months at 12% compounded semi-annually. Which is lower: the cash price or the present value of the installment?

15. FAIR MARKET VALUE CASH FLOW – is a term that refers to payments received (cash inflows) or payments or deposits made (cash outflows). Cash inflows can be represented by positive numbers and cash outflows can be represented by negative numbers. FAIR MARKET VALUE of a cash flow (payment stream) on a particular date refers to a single amount that is equivalent to the value of the payment stream at that date. This particular date is called the focal date .