Annuities Quarter 2 Week 3 PDF

ANNUITIES QUARTER 2 – WEEK 3 Give an example of a situation where a payer makes payments by installment.  ANNUITIES It is the series of equal payments or withdrawal in an equal length periods. The equal payment is called periodic rent. Amount of annuity is the sum of all pay...

ANNUITIES QUARTER 2 – WEEK 3 Give an example of a situation where a payer makes payments by installment.  ANNUITIES It is the series of equal payments or withdrawal in an equal length periods. The equal payment is called periodic rent. Amount of annuity is the sum of all payment.  ANNUITIES ACCORDING TO SIMPLE ANNUITY GENERAL ANNUITY PAYMENT An annuity where the An annuity where the payment interval is the payment interval is not INTERVAL AND same as the interest the same as the interest INTEREST PERIOD period. period. ACCORDING TO ORDINARY ANNUITY ANNUITY DUE TIME OF PAYMENT A type of annuity in which A type of annuity in which the payments are made the payments are made at the end of each at the beginning of each payment interval. payment interval. ACCORDING TO ANNUITY CERTAIN CONTINGENT ANNUITY DURATION An annuity in which An annuity in which the payments begin and end payments extend over an at definite terms. indefinite or undetermined length of time 1. Rene would like to pay the installment for the car at the end of each month, that is 9% compounded monthly.SIMPLE ANNUITY 2. Carl would like to pay the installment for the washing machine at the end of each month, that is 9% compounded annually. GENERAL ANNUITY 3. Ana would like to save money for college at the end of each month, that is 7.5% compounded quarterly. GENERAL ANNUITY 4. Bona would like to save money for college at the end of each quarter, that is 1.25% compounded quarterly.SIMPLE ANNUITY 1. Monthly rent payments are made at the ANNUITY DUE beginning of each month. 2. A company pays its employees' retirement contributions at the end of each period. ORDINARY AN 3. A person deposits money at the beginning of every quarter for a savings plan. ORDINARY ANNUITY 4. Insurance premiums are paid at the start of each year. ANNUITY DUE 5. A loan payment is made at the end of each month.ORDINARY ANNUITY  SIMPLE ANNUITY GENERAL ANNUITY ORDINARY ANNUITY DUE ORDINARY ANNUITY DUE ANNUITY ANNUITY FUTUR [ [ ] ] [ ] [ ] 𝑛 𝑛 𝑛 ( 1+𝑖) −1 𝑛 ( 1+ 𝑖 ) − 1 (1+ 𝑝) − 1 ( 1+𝑝 ) − 1 E 𝐹𝑉 𝑂𝐴 = 𝐴 𝑖 𝐹𝑉 𝐴𝐷 = 𝐴 𝑖 (1+ 𝑖) 𝐹𝑉 𝑂𝐺𝐴 = 𝐴 𝑝 𝐹𝑉 𝐺𝐴𝐷 = 𝐴 𝑝 (1+𝑖) VALUE PRESE [ [ ] ] [ ] [ ] −𝑛 1− ( 1 +𝑖 ) −𝑛 1 − ( 1+𝑖) 𝑛 1 − (1+𝑝 ) −𝑛 1 − ( 1+𝑝 ) NT 𝑃𝑉 𝑂𝐴 = 𝐴 𝑃𝑉 𝐴𝐷 = 𝐴 𝑖 𝑖 𝑃𝑉 ( 1 𝑂𝐺𝐴 𝐴 𝑖) =+ 𝑝 𝑃𝑉 𝐺𝐴𝐷 = 𝐴 𝑝 (1 +𝑖) VALUE  FUTURE VALUE AND PRESENT VALUE OF SIMPLE ANNUITY A = equal payments n = number of compounding j = periodic interest rate m = number of compounding periods i = the periodic rate of payments ()  EXAMPLE 1. Find the future value of series of payments of Php 918 made at the end of every quarter for 4 years if the interest rate is 4.8% compounded quarterly.  EXAMPLE 2. Find the future value of series of payments of Php 918 made at the beginning of every quarter for 4 years if the interest rate is 4.8% compounded quarterly.  EXAMPLE 3. Find the present value of series of payments of Php 850 made at the end of every month for 2 years if the interest rate is 2% compounded monthly.  EXAMPLE 4. Find the present value of series of payments of Php 850 made at the beginning of every month for 2 years if the interest rate is 2% compounded monthly.  SIMPLE ANNUITY GENERAL ANNUITY ORDINARY ANNUITY DUE ORDINARY ANNUITY DUE ANNUITY ANNUITY FUTUR [ [ ] ] [ ] [ ] 𝑛 𝑛 𝑛 ( 1+𝑖) −1 𝑛 ( 1+ 𝑖 ) − 1 (1+ 𝑝) − 1 ( 1+𝑝 ) − 1 E 𝐹𝑉 𝑂𝐴 = 𝐴 𝑖 𝐹𝑉 𝐴𝐷 = 𝐴 𝑖 (1+ 𝑖) 𝐹𝑉 𝑂𝐺𝐴 = 𝐴 𝑝 𝐹𝑉 𝐺𝐴𝐷 = 𝐴 𝑝 (1+𝑖) VALUE PRESE [ [ ] ] [ ] [ ] −𝑛 1− ( 1 +𝑖 ) −𝑛 1 − ( 1+𝑖) 𝑛 1 − (1+𝑝 ) −𝑛 1 − ( 1+𝑝 ) NT 𝑃𝑉 𝑂𝐴 = 𝐴 𝑃𝑉 𝐴𝐷 = 𝐴 𝑖 𝑖 𝑃𝑉 ( 1 𝑂𝐺𝐴 𝐴 𝑖) =+ 𝑝 𝑃𝑉 𝐺𝐴𝐷 = 𝐴 𝑝 (1 +𝑖) VALUE  FUTURE VALUE AND PRESENT VALUE OF GENERAL ANNUITY A = equal payments n = number of compounding j = periodic interest rate m = number of compounding periods i = the periodic rate of payments () c = number of interest conversion periods per payment interval  EXAMPLE 1. Find the future value of series of payments of Php 918 made at the end of every quarter for 4 years if the interest rate is 4.8% compounded annually.  EXAMPLE 2. Find the future value of series of payments of Php 918 made at the beginning of every quarterly for 4 years if the interest rate is 4.8% compounded annually.  EXAMPLE 3. Find the future value of series of payments of Php 850 made at the end of every month for 2 years if the interest rate is 6% compounded semi-annually.  EXAMPLE 4. Find the present value of series of payments of Php 850 made at the beginning of every month for 2 years if the interest rate is 6% compounded semi- annually.  ACTIVITY #3 Find the future and the present value of the following: 1.Payment of Php 1,020 at the beginning of each month for 4 years with annual interest of 7.2% compounded annually savings. 2.Deposit of Php 1,950 at the end of every quarter for 4 years with an annual interest of 6% annually compounded monthly 3.Savings of Php 1,750 at the end of every 3 months for 4.5 years with annual interest of 6% compounded semi-annually. 4.Deposit of 1055 at the beginning of every quarter for 8 years with annual interest of 4% compounded quarterly 5.Savings of 2,500 at the end of every 6 months for 10 years with annual interest of 6% compounded semi-annually.