CASIO 9860 Manual
Contents
1. It is what we want to know so it makes no difference what number is entered here PV is negative because 12000 left your pocket PMT 0 there were no regular payments FV is positive because 18000 will return to your pocket in the future P Y and C Y 1 the interest compounds once a year P Y and C Y are always equal Now press F2 for the interest rate Fig6 FU 9855 BB5542 n tx ev FMT Fe Gia Casio 9860 Graphic Calculator Self Guided Instructions TVM Mode Richard Andrew Stuart Palmer 2008 3 Press EXIT to view solution in previous screen Fig7 DA Dee CEO IFAT Cr Below is an example that involves repeated investments an annuity that receives compound interest Example la A sum of 2 000 is invested at the end of every year at 8 pa interest compounded yearly for 20 years What is the future value of this investment Enter the values as they appear in the question pressing EXE after each entry Check your entries with Fig8 NOTES n 20 years 1 8 in TVM the interest is always pa PV 0 the annuity started with nothing PMT is negative each payment leaves your pocket FV CAN BE ANYTHING It is what we want to know so it makes no difference what number is showing here est P Y and C Y 1 the interest compounds once a year P Y and C Y are always equal FU 91523 9286 Now press F5 for FV Fig9 akFH Press EXIT Fig10 Comeound Interest End Note that FV is posit2. TVM protocols to be used are n number of time intervals could be 8 years or 32 quarters or 96 months I1 the per annum interest rate as a percentage eg 11 5 is entered as 11 5 not 0 115 PV Present Value PMT Payment per time period FV Future Value P Y It is best to consider both P Y and C Y as the number of compounding periods per year ie both values will always be identical P Y is meant to stand for payments year but this does not make sense for this protocol C Y Same as P Y Eg If the investment or loan is compounding annually once per year then P Y C Y 1 If the investment or loan is compounding quarterly 4 times per year then P Y C Y 4 If the investment or loan is compounding monthly 12 times per year then P Y C Y 12 NOTE The dollar values PV PMT and FV need to be entered either as positives or negatives depending on the situation This seems confusing at first but is actually very simple Consider each situation to be money either LEAVING your pocket OR RETURNING to your pocket e f money is LEAVING your pocket the number is entered as a negative e f money is returning to you the number is entered as a positive Therefore e receiving a loan of 5000 PV 5000 e aregular payment from you of 260 PMT 260 e investing 50 000 PV 50 000 e an investment that will be worth 100 000 in 10 years time FV 100 000 Casio 9860 Graphic Calculator Self Guided Instruc
3. the formulae From experience when teaching TVM protocols if the formulae protocols are referred to simultaneously students understand quickly and with little confusion Over the long term these differences prove to be a very minor disadvantage when compared to the ease and versatility of using TVM TVM Graded Question Series The Financial_Maths_TVM_Sheets 1 3 are an excellent graded worksheet series with solutions designed for students to gain practice in using TVM For further and more advanced information including practice questions refer to the manual Mathematics with a Graphics Calculator Casio fx 9860 AU by Barry Kissane amp Marian Kemp available at http www casioed net au downloads books fx9860 orderBarryBook pdf ComFound Interest PU 19636 29451 4 Pu 19636 29451 z eee A ts eS Fat Tre Casio 9860 Graphic Calculator Self Guided Instructions TVM Mode Richard Andrew Stuart Palmer 2008 5
4. Casio 9860 Self Guided Instructions TVM Mode Instructions Screenshots Using TVM TVM stands for Time Value Money TVM is the Financial Mode on the calculator However Financial Mathematics questions can also be performed in RUN EQUA and SSHT modes TVM is fantastic for investigating financial scenarios and is very easy to use when dealing with annuity investment and loan scenarios However it is important to realize TVM is essentially a black box a number in number out machine It is therefore mathematically wise to expose students to using at least RUN and EQUA in addition to TVM when dealing with financial mathematics over the full duration of a course There are excellent PD resources at http www casioed net au services tuition fx9860 fx9860_tuition php which include easy to follow worksheets instructions and videos on financial mathematics which deal with RUN EQUA and SPREADSHEET Modes Below are instructions that will get you started with TVM There are different sets of protocols by which TVM can be used The protocol outlined below is very easy to follow Press MENU scroll to TVM EXE then press F2 for Compound Interest Fig1 Note that numbers will appear on this screen from previous calculations Pay no attention to these numbers y A fis FY FAT Try Casio 9860 Graphic Calculator Self Guided Instructions TVM Mode Richard Andrew Stuart Palmer 2008 1 The
5. ive not negative because after 20 years the investment goes back into your pocket A The investment was 2000 x 20 which is 40 000 MT 2006 FU 91523 9256 Pev 1 The investment has grown from 40 000 to 91 523 93 to the nearest cent Da Ix GL Ga GT Example 1b What is the present value of the annuity in example la OR What single investment earning the same rate of compound interest for 20 years would give the same future value as the repeated investments in example la Enter the values as they appear in the question pressing EXE after each entry Check your entries with Fig11 oar pe BAT FT Casio 9860 Graphic Calculator Self Guided Instructions TVM Mode Richard Andrew Stuart Palmer 2008 4 NOTES All that needs to change from the Qla entries is PMT to be changed to zero The FV for 1b is the same FV as in 1a Now press F3 for PV Present Value See Fig12 Press EXIT to view in original screen Fig13 Note that PV is negative not positive because the money is leaving your pocket to make the single investment A single investment of 19 636 29 NOW will produce the same result in 20 years Don t students get confused when being taught TVM because values have to entered differently to the formulae This is a question often asked by teachers learning TVM The main difference of course is that interest rates need to be entered as whole pa percentages into TVM but as per time period decimals in
6. tions TVM Mode Richard Andrew Stuart Palmer 2008 2 Below are two examples that involve a once only investment that receives compound interest Example 1 A sum of 2 000 is invested at 8 pa interest compounded monthly for 20 years What is the future value of this investment Enter the values as they appear in the question pressing EXE after each entry Leave FV as the pre existing value Check your entries with Fig2 NOTES n 20x12 is the number of months A good habit for students to enter n as eg 20x12 so as to minimize careless error 1 8 in TVM the interest is always pa PV is negative because 2000 left your pocket PMT 0 there were no regular payments FV CAN BE ANYTHING It is what we want to know so it makes no difference what number is showing here P Y and C Y 12 the interest compounds 12 times every year P Y and C Y are always equal Now press F5 for FV Future Value See Fig3 The answer can be read in the previous screen by pressing EXIT Fig4 Note that FV is positive not negative because after 20 years the investment goes back into your pocket The investment has grown from 2000 to 9853 61 Example 2 What annual interest rate will be required for an investment of 12 000 to become 18 000 in 5 years if the interest compounds annually Enter the values as they appear in the question pressing EXE after each entry Check your entries with Fig5 NOTES n 5 years I ANYTHING
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CASIO 9860 Manual