TO BE ANSWERED (ACTIVITY 1 ONLY):

FINAL KNOWLEDGE: Generalization/ Synthesis/ Summary In the previous lesson we tackle about annuity where the sum of all payments of the annuity is at the end of the last interest conversion period. How about in the general annuity? How to differentiate from simple annuity from general annuity? In general annuity we focus on the computation of deferred annuity, present value and future value of deferred annuity, general ordinary annuity, present value of general annuity due, future value of general annuity due. Different examples are given for more understanding of the lesson. Based on the given sample problems you can identify which formula are you going to use in each situation. REVISED KNOWLEDGE: Actual answer to the process questions/ focus questions 1. How to solve for the future value and present value of general annuities? 150- 2 on28 = V In solving for the future and present annuity you can use the formula 50.0 VI Present Value of General Ordinary Future Value of General Ordinary Annuity .Annuity slumol pv = (1+1) FV =P CL+0 (1 + 1 ) - 1 where P = regular payment i = rate per conversion period (i - K - no. of conversion periods in a annual rate n=number of conversion periods for the whole term (n = t . K, where t is the term of an annuity) "where p is the number of months in a payment interval and c is the number of months in a compounding period. 2. Difference of general annuity from general annuity due. buon flew maxsine aMi Ena 14 Jogsb /dinoin gnidam yo General annuity is an annuity where the payments do not coincide with the interest periods while general annuities due are annuities where payments are made at the beginning of each period but the compound period is not equal to the payment period. 000 ,0OE -VExample 3. P25, 000.00 will be invested in an account at the end of each year at 4% compounded semi-annually. Find the size of the fund at the beginning of the 16" year. SOLUTION: Given: P=25, 000 C-6 =15 K=2 b= 2 = 12 = 2 Ba. Feb. 18 = Vq 1=15(2) = 30 2 = 0.02 PV = p (1+i) "-1, PV = 25, 000 (1+0.04)-30-1] L (1+0.04)2-1. = P502,080.19 PRESENT VALUE of GENERAL ANNUITY DUE so) o"a to ster levisin when bain annoy 2 FORMULA where PV = Present value orli as an102 FV # Future P =Annuity Payment Dani momzeq C - annual rate i z rate per compounding period ( = K - no. of conversion periods in a year n = number of conversion period (n = t . K, where t is the term of an annuity c.= number of months in a compounding period : p - number of months in a payment interval, YiluonA - Vq Examples ni abuiton noisravn bonsq nommovnos ing atm = 1. Find the present value of an annuity due of P10, 000 payable quarterly for 10 years if money is worth 6% compounded semi-annually. SOLUTION wun or 21 5 ban Invaini Inomeng a ni edinot to 15dmon ash ai quistwe Given: P=10, 000 C=6 .boizon quibnoquigg a ni arunon 10 1= 10 years p=3 K=2 b= = = = 0.5 A vianibIO Improv To SulaV in52571) 29.19MAXa zi vonorn=10(2)-20, @ roil vilsunina olderng 00051 to whoruns visnibio ne to sulsv inseong orit bail .I i= !_ 6% = 0.03 Schohsup bobauogmoo ofe now K PV = p 1-(1+i)-" MOITUJO2 (1+16-1 + i 00054 9 :navid PV = 10000 1-(1+0.03)-20 0.03 + 0.03 0.03 (1+0.03)05-1 PV= 304, 227.87 Present Value of General Annuity Due with Down Payment (25 10 0+1)-1 0008 = Vq 2. Mrs. Samson bought a brand-new car for P500, 000 down payment and P20, 000.00 every first day of each month for 3 years. If payments are based on 8% compounded semi-annually, what is the total cash price of the car? SOLUTION Given: hittip loss To bes views 00.0904 bra fromcan awob 00.0002 101 elle snordaliso restal salT .S DP=P500, ooo Insleympo deno ath burd gusone-irse bobouogmos off to stan sil ia NOTTU.102 P=P20,000 ulay inseong aris bus (() inomean "web ardi bbs (8)) inslaviups rass sch may of 1=3 years 6 novig 9in ow . V4 10 K=2 n=3(2) 00.0009 i= 1= 3% or 0.04 PV = p (1-(1+0)-"] 4 + 1 2.0 = = =9-d 100 = Jazz late-1 PV = p 1-(1+0.04)-51 0.04 0.04 + 0.04 = 643,654.45 L(1+0.04)6-1 Total Cash Price = DP + PV = P500, 000 + 643,654.45 = PI, 143, 654.45To visualize and find d, we have; ist payment (P,) 32- 2 3 5 6 7 8 10 11 PV = ppl-(1+1)-("a) 000 25-4 novill _ 1-(1=1)-d 1= 1500(1-(1+0.015)-(32412) ( 1-(140.015)-12 PV = 31,699.68 0.015 0.015 50.0 = EXERCISES: Do what is asked er.080,song (8909 500 25 = 13 1. A deferred annuity is purchased that will pay P5,000 per quarter for 10 years after being deferred for 5 years and with interest rate of 6% compounded quarterly. What is the Present Value of the annuity? AJUMNOT General Annuity General Annuity- is an annuity wherein the interest conversion period is unequal or not the same as the payment interval thomend vienna sim Inner - GENERAL ORDINARY ANNUITY Present Value of General Ordinary : Future Value of General Ordina Annuity Annuity PV = P ( 1 + 1)= 1 where P = regular payment - annual rate j = rate per conversion period ( 7 K- no. of conversion periods in n =number of conversion periods for the whole term (net/ K, where t is the term am ber i "of an annuity) "where p is the number of months in a payment interval and c is the number .102 of months in a compounding period. 000 .01 4 navid EXAMPLES (Present Value of General Ordinary Annuity) 1. Find the present value of an ordinary annuity of P2000 payable annually for 9 years if the money is worth 5% compounded quarterly? 80.0 =-- SOLUTION: Given: P=P2000 C= 3 1-80+1) n=9(4)=36 P250.9 + EO.0 (ex-(20.0+1)-4 00001 = Va i = ! _ 5% = 0.0125 b=P _ 12 = 4 "(10.0+ 1)! EO. 574.16 PV = 2000 1-(1+0.0125)-361 lasmys'l norod shiw sul giunA loaned to saint insert L (1+0.0125)4-1 10 py - 14,155.99 TOus momenq nwob 000 .002 101 mo won-band s idgood noeme? AM S "vilsunns-imse bobmoqmo9 808 no boand sis amonring 'll anov & sol dinom docs Example of Present value of General Ordinary Annuity with Down Payment $hao sed to song 2. The latest cellphone sells for 5000.00 down payment and P900.00 every end of each quarter for 3 years at the rate of 8% compounded semi-annually. Find the cash equivalent of the cell phone. SOLUTION To get the cash equivalent (CE), add the down payment (D) and the present value (PV) For PV, we are given: P= P900.00 C-6En n=3(2) = 6 p=3 10.0 To = 1 9 K i = _ _ 3 = 0.04 2 b= P = 2 = 0.5 (1+1)-" PV = PL- (1+06-1 PV = 900 -(1+0.04)- (1+0.04)0.5_ = P9529.28 CE = DP + PV - 900 + 9529.28 =P14 529 28 008 = V + 40 = sami sand InaTA. Written Work/s ACTIVITY 1 Directions: Solve the following problems. 1. Your mom decided to join their office cooperative (an organization owned and run by bits members who share profits and benefits) and agreed to contribute P 1,000 per month beginning in January 2019 which will earn 3% interest compounded monthly. How much will be the future value of your mom's contribution at the end of April 2019? 2. Your dad applied for a term life insurance (provides the insured person with a coverage for a specified period of time of one, five or more years), He got a flexible policy (allows the insured person to change certain components of the insurance plan) because some payment options include a policy payout (insurance proceeds) as soon as the target period achieved or upon contingency (death or accident). Some companies offer insurance products that can be availed only upon death. Because of this better option, your dad decided to avail of insurance A's flagship insurance product, Your dad's contribution per year is P20,090 that earns 6% compounded monthly for 20 years. How much will be paid out to your dad after 20 years by insurance A?Deferred Annuity A deferred annuity is an annuity in which the first payment is not made at the beginning nor at the end of the payment interval but at a later date. The length of time when these payments are made is called the period of deferment. The first payment is made one period after the period of deferment. Thus, the annuity that is deferred for six periods will have the first payment at the end of 7 periods. Likewise, in an annuity whose first payment is made at the end of the 7 periods, the annuity is deferred for,6 months. PRESENT VALUE AND FUTURE VALUE OF DEFERRED ANNUITY The present value PV of a deferred annuity is given by the formula al where py = Present Values p =Regular payment i = rate per conversion period( period . where's is the annual rafe and K is the number of conversion periods = number of paying periods (n = to K where | is the number of years) number of deferre The future value PV of a deferred annuity is given by the formula: most off binblind sonammoho stangorges gniew estrune tions FV = p (1+1= Aaronomit brin easalaud where UNION ONT FV = Future Value P = Regular payment him aity, Nowlad i = rate per conversion period (i = 7. where r is the annual rate and K is the number of conversion periods) 25016V 9103 n = number of paying periods (n = t : K, where t is the number of years) ;on) Note: the future value of a deferred annuity is the same as the future value of simple ordinary annuity. Examples LOLIC: DEREKRED 1. Find the present value of 10 semi-annual payments of P2,000.00 each if the first payment is due at the end of 3 years and money is worth 8% compounded semi-annually. SOLUTION Given: P= 2,000 1= 5 :29viloojdO ohio9q2 \\alogsT gaimas I will ous welsad 1= 8% i= 8%/2= 0.04 K=2 n= 5(2) = 10 .vliunins bonslob smiled .[ To visualize and find d, we have finis Imonigg to oulav insaoiq bas sulsy annul orhi bail .S 1ST PAYMENT sub vimunns Isionsg lo sulsv tasesiq oril 101 svloe .& sub vimunns intoup to sulav sulu ord gnininnsisb ni slurmol sill viggA A P. P, P P, P. P. WP, I roil to noisolqad -O- 2 3 injog 4 d=5 (circles with x) PV = ppl-(1+1)-("d) _1-(1=1)-d -1 = 2000[1-(1+0.04)-(10+5) 1-(1+0.04)-5, 0.04 0.04 PV = 13, 333.13 2. Find the Present Value of a deferred annuity of P1,500 every3 months for 8 years that is deferred 3 years if money is worth 6% converted or compounded quarterly. SOLUTION Given: P=1500 1= 8 years oozestaff Positions ed lis monsq 15 8(redmomas binode nog modi anoitesup sbing you adi n wood K =4 d=3(4)=12 sow orb to bris and is moth rowans of side ed bluada goY i= 6%/4=0.0015 Casinonns imoney to sulev mseen bas oulav awful or not avior of wollFUTURE VALUE OF GENERAL ANNUITY DUE Example: Emy wants to save P100,000 for her first year college. She deposits P3500 at the beginning of each month in an years? account that earns 4% per year compounded semi-annually. Will Emy have enough money saved at the end of 2 SOLUTION Given: P= 3500 C 6 n= t(K) = 2(20 =4 p=1 i =! = 40 = 0.02 2 FV = p ((1+0 "-1] FV = 3500 (1+0.02) 4-1 0.02 0.02 (1+0.02)6-1 - + 0.02 FV= P87,529.40 Since 87,529.40 is less than 100,000, Emy will not have enough money at the end of 2 years Regular Payment (P) of General annuity To solve for P in the formula for PV and FV for general Annuity, we can transform the formula as follow; For General Annuity, (1+ i) -1 P =PV (1+i) - 1 1 -(1 +1)- P = EV (1+1)-1 EXAMPLE 1. Mr. and Mrs. Salazar will need P300,000 in 2 years to start their own business. They plan to save money by making monthly deposits at the end of each month in an account earning 8% per year compounded quarterly. How much must they make monthly? Ford contour SOLUTION: Digg ingmeta pit of laups Jon at bang GIVEN: FV= 300, 000 P= 1 n=tK= 2(4)=8 b= 2 6 4 I _ 890 = 0.02 (FV)|(1+10-1] (1+i)"-1 (300,000) (1+0.02)6-1 P = (1+0.02)8-1 = P1 1,574.16 2. A couple left their son with a P1,000,000.00 insurance policy. What monthly income would the policy provide for 15 years if the insurance company pays 8% compounded semi-annually? SOLUTION Given: PV=P1000,000 p=1 n=1K= 15(2)=30 C= 6 i=! K or 0.04 b=2 = 1 6 = 1000,000 (1+0.04)2-1 1-(1+0.04)-30] = P9,481.53