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# TVM Annuities Morning CSR 342

Purdue

GPA 2.6

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This 10 page Class Notes was uploaded by feichen on Thursday March 5, 2015. The Class Notes belongs to CSR 342 at Purdue University taught by m in Fall. Since its upload, it has received 62 views.

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Date Created: 03/05/15

Annuity Equations 22 Compounding e FVACFxFVFA 22 Where 22 Discounting e PVACFxPVFA 1 121 i 12 1 1 n quot6 Where 0 An Important Annuity Feature 32 PVA is alwaya located one period efore the rst CF 32 FVA is alwaya located at the mat CF period CF gt CFAICFA CFA CFA CFA CFA t 3 t 2 t 1 t0 t1 t2 t3 t4 I PVA FVA 2 I TVM Annuities Morningnb Annuity Examples 0 You took out a loan that you ll be making payments of 1600 annually on for the next 5 years with an interest rate of 4 Two questions a What is the present value of the loan amount you borrowed a What is the future value of the loan amount you ll need to pay back Steps What are the PV t0 and FV t5 of the following i400 n5 CF1600 PVA FVA I1 CF 0 4 5 l 6 0 0 a 1 Show the locations of known and unknown variables W 1600 1600 1600 1600 l1600 et0lt1lt2t3t4lt5 a 2 Substitute known values into the formulas PVA CF x PVFA and FVA CF x FVFA 1 1 1z PVFA a i Find PVA and FVFA 1 1 1zyl a a 1 1045 04 0mm 445 18223 TVM Annuities Morningnb I 3 1600 4 451822331016212 0mm 71229157 quot2 b PVA1600x44518 gt quot2 ii Find FVA a a FVFA 1 045 1 04 a b FVACFxFVFA gt FVA160054163 In51 1600 541632 Out51 8666112 4 I TVM Annuities Morningnb Your turn You took out a loan on which you ll be making annual payments of 1500 for 4 years The interest rate is 57 What is the future value of this loan FVFA FVA CF FVFA 1 0374 1 037 6341 29 1500 TVM Annuities Morningnb I 5 Annuities Example 2 a What happens when we have two annuities The first cash ow CF1 of 300 starts at period 2 and lasts for 3 consecutive periods and the second cash flow CF2 of 500 begins immediately after CF1 ends and lasts for another 3 periods a What is the value of these cash ows today t0 Assume a 5 interest rate Solution CFl n1 CF2 n2 300 3 500 3 05 And CF1 begins at period 2 a 1 Illustrate the locations of the known and unknown variables 300300300 500 500 500 t0l1l2l34l5l67 a 2 Find the value of CF1 at t0 1 1 1mm a i Insert known values into PVA for CF1 PVACFgtlt m 1053 05 2723248 PVAl 300 2723248 81697 44 2 ii What time is it located t1 Fv1 PVA1 1i 1 1i 1 2 iii Discount it to the appropriate time using PV1 6 I TVM Annuities Morningnb 8169744 PV1 1 05 1 778 07086 TVM Annuities Morningnb I 7 And now we start on the second cash ow CFl n1 CF2 n2 i PVA 300 3 500 3 05 300 30039300 500 500 500 t0l1l2l34l5l67 quot392 3 Find the value of CF2 at t0 CF2 begins after the first period 1 1 1Z 2 quot392 1 Insert known values into PVA for CF1 PVACFgtlt 1053 mm PVAZ 05 0 2723248 mm 500 2723248 1361 624 quot392 ii What time is it located t4 2 2 quot392 iii Discount it to the appropriate time using PV2 1 HW 1 02 1361624 1 054 11202114345360214 quot392 4 Add the present values of both cash ows CFs to find PVA may 11202114 778070857142857 1898 2823 n12 PV2 Printed by Wolfram Mathematica Student Edition 8 I TVM Annuities Morningnb Your Turn The first cash ow CF1 of 800 starts at period 5 and will last for 4 con secutive periods The second cash ow CF2 of 4 00 will begin immedi ately after CF1 ends and lasts for another 5 periods What is the value of these cash ows today t0 Assume a 7 annual interest rate Hint Figure out the timeline first 800 800 800 800 400 400 400 400 I 400 t0itzlitzit3it4it5it6 tz7 tz8 tz9 tzloitzll 1 1 510724 510725 07 07 1 072 1 076 Out14 34596711 1 1 1 394 Steps PVA of the first cash ow PVA 2 CF PVA Then nd the present value of that PV1 1 0 1 1 395 P A Then do it over again for the second cash ow PVA 2 CF gt PV2 L And add both together PV1 PV2 TVM Annuities Morningnb I 9 And One More Annuity Example 1quot How much would you have to deposit each month into an account that earns 4 interest compounded monthly if you wanted to have 20000 four years from now Your first deposit will be one month from now and your last 4 8 months from now i 04n4m12FVA20000CF iquot 1 Find frequency of compounding amounts 2amp mgtltn iquot im gt0412 gt 0033 iquot mxn gt4x12 48 iquot 2 Find FVFA using the frequency of compounding amounts found in step 1 a FVACFXFVFA where FVFA1 3 1 1 003348 1 0033 m FVFA 5 1 917954 1quot We want to find CF so change FVACFxFVFA into CF 1quot Plug in the numbers we have and solve for CF 20000 n16 51917954 mm 38522 48 00017 1849056 10 I TVM Annuities Morningnb And Your Turn How much would you have to deposit each month into an account that earns 5 interest compounded monthly if you wanted to have 5000 in five years from now Your first deposit will be one month from now and your last 60 months from now 5000 10312lt5gtlt12gt 1 0312 om51 77343453

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