HP 10BII Manual
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3: Number Storage and Arithmetic 41 Doing Arithmetic Inside Registers
42 3: Number Storage and Arithmetic Doing Arithmetic 0DWKIXQFWLRQVRSHUDWHRQWKHQXPEHULQWKHGLVSOD\ Example. &DOFXODWHWKHQFDOFXODWH Example. &DOFXODWHQDWXUDOORJDULWKPH\f7KHQFDOFXODWH Keys: Display: Description: *[0.25&DOFXODWHVWKH UHFLSURFDORI *T4.47&DOFXODWHVÖ 51.67&DOFXODWHV Ö *h1.21&DOFXODWHV 52.88&RPSOHWHVWKH FDOFXODWLRQ Keys: Display: Description: * 12.18&DOFXODWHVH *?2.50&DOFXODWHVQDWXUDOORJD ULWKPRIWKHUHVXOW *e24.00&DOFXODWHVIDFWRULDO 814.00&RPSOHWHVFDOFXODWLRQ 10B.book Page 42 Wednesday, June 21, 2000 5:19 PM
3: Number Storage and Arithmetic 43 Power Operator 7KHSRZHURSHUDWRU*^UDLVHVWKHSUHFHGLQJQXPEHU \ YDOXH\fWRWKHSRZHURIWKHIROORZLQJQXPEHU [YDOXH\f Example. &DOFXODWHWKHQILQGWKHFXEHURRWRI Using Parentheses in Calculations 8VHSDUHQWKHVHVWRSRVWSRQHFDOFXODWLQJDQLQWHUPHGLDWHUHVXOWXQWLO \RX·YHHQWHUHGPRUHQXPEHUV
44 3: Number Storage and Arithmetic 7RGHOD\WKHGLYLVLRQXQWLO\RX·YHVXEWUDFWHGIURPXVHSDUHQWKHVHV &ORVLQJSDUHQWKHVHVDWWKHHQGRIWKHH[SUHVVLRQFDQEHRPLWWHG)RU H[DPSOHHQWHULQJ´¸ ï µLVHTXLYDOHQWWR´ ¸ ï \f\f µ Keys: Display: Description: d* 85.001RFDOFXODWLRQ\HW *73.00&DOFXODWHV² 0.41&DOFXODWHV ¸ 3.700XOWLSOLHVWKHUHVXOWE\ .book Page 44 Wednesday, June 21, 2000 5:19 PM
4: Picturing Financial Problems 45 4 Picturing Financial Problems How to approach a Financial Problem 7KHILQDQFLDOYRFDEXODU\RIWKH+3%,,LVVLPSOLILHGWRDSSO\WRDOO ILQDQFLDOILHOGV)RUH[DPSOH\RXUSURIHVVLRQPD\XVHWKHWHUPEDODQFH EDOORRQSD\PHQW UHVLGXDO PDWXULW\YDOXH RUUHPDLQLQJDPRXQW WRGHVLJQDWHD YDOXHWKDWWKH+3%,,NQRZVDV /IXWXUHYDOXH\f 7KHVLPSOLILHGWHUPLQRORJ\RIWKH+3%,,LVEDVHGRQFDVKIORZ GLDJUDPV&DVKIORZGLDJUDPVDUHSLFWXUHVRIILQDQFLDOSUREOHPVWKDW VKRZFDVKIORZVRYHUWLPHUDZLQJDFDVKIORZGLDJUDPLVWKHILUVWVWHS WRVROYLQJDILQDQFLDOSUREOHP 7KHIROORZLQJFDVKIORZGLDJUDPUHSUHVHQWVLQYHVWPHQWVLQDPXWXDO IXQG7KHRULJLQDOLQYHVWPHQWZDVIROORZHGE\LQYHVWPHQWVRI DQGDWWKHHQGRIWKHWKLUGDQGVL[WKPRQWKV$WWKH HQGRIWKH WKPRQWKZDVZLWKGUDZQ$WWKHHQGRIWKHWK PRQWKZDVZLWKGUDZQ 10B.book Page 45 Wednesday, June 21, 2000 5:19 PM
46 4: Picturing Financial Problems $Q\FDVKIORZH[DPSOHFDQEHUHSUHVHQWHGE\DFDVKIORZGLDJUDP$V \RXGUDZDFDVKIORZGLDJUDPLGHQWLI\ZKDWLVNQRZQDQGXQNQRZQ DERXWWKHWUDQVDFWLRQ 7LPHLVUHSUHVHQWHGE\DKRUL]RQWDOOLQHGLYLGHGLQWRUHJXODUWLPHSHULRGV &DVKIORZVDUHSODFHGRQWKHKRUL]RQWDOOLQHZKHQWKH\RFFXU:KHUHQR DUURZVDUHGUDZQQRFDVKIORZVRFFXU Signs of Cash Flows ,QFDVKIORZGLDJUDPVPRQH\LQYHVWHGLVVKRZQDVQHJDWLYHDQGPRQH\ ZLWKGUDZQLVVKRZQDVSRVLWLYH&DVKIORZLQJRXWLV QHJDWLYH FDVKIORZLQJ LQ LV SRVLWLYH )RUH[DPSOHIURPWKHOHQGHU·VSHUVSHFWLYHFDVKIORZVWRFXVWRPHUVIRU ORDQVDUHUHSUHVHQWHGDVQHJDWLYH/LNHZLVHZKHQDOHQGHUUHFHLYHVPRQH\ IURPFXVWRPHUVFDVKIORZVDUHUHSUHVHQWHGDVSRVLWLYH,QFRQWUDVWIURP WKHERUURZHU·VSHUVSHFWLYHFDVKERUURZHGLVSRVLWLYHZKLOHFDVKSDLG EDFNLVQHJDWLYH 12345678910111213141516 -5,000.00 -6,000.00 16,567.20 5,000.00 -7,000.00 The horizontal line represents time. It is divided into regular periods. Up-arrows represent positive cash flows (money received). Down-arrows represent negative cash flows (money paid out). 10B.book Page 46 Wednesday, June 21, 2000 5:19 PM
4: Picturing Financial Problems 47 Periods and Cash Flows ,QDGGLWLRQWRWKHVLJQFRQYHQWLRQFDVKIORZLQJRXWLVQHJDWLYHFDVK IORZLQJLQLVSRVLWLYH\fRQFDVKIORZGLDJUDPVWKHUHDUHVHYHUDOPRUH FRQVLGHUDWLRQV n7KHWLPHOLQHLVGLYLGHGLQWRHTXDOWLPHLQWHUYDOV7KHPRVWFRPPRQ SHULRGLVDPRQWKEXWGD\VTXDUWHUVDQGDQQXDOSHULRGVDUHDOVR FRPPRQ7KHSHULRGLVQRUPDOO\GHILQHGLQDFRQWUDFWDQGPXVWEH NQRZQEHIRUH\RXFDQEHJLQFDOFXODWLQJ n7RVROYHDILQDQFLDOSUREOHPZLWKWKH+3%,,DOOFDVKIORZVPXVW RFFXUDWHLWKHUWKHEHJLQQLQJRUHQGRIDSHULRG n,IPRUHWKDQRQHFDVKIORZRFFXUVDWWKHVDPHSODFHRQWKHFDVK IORZGLDJUDPWKH\DUHDGGHGWRJHWKHURUQHWWHG)RUH[DPSOHD QHJDWLYHFDVKIORZRI²DQGDSRVLWLYHFDVKIORZRI RFFXUULQJDWWKHVDPHWLPHRQWKHFDVKIORZGLDJUDPDUHHQWHUHGDVD FDVKIORZ² \f n$YDOLGILQDQFLDOWUDQVDFWLRQPXVWKDYHDWOHDVWRQHSRVLWLYHDQGRQH QHJDWLYHFDVKIORZ Simple and Compound Interest )LQDQFLDOFDOFXODWLRQVDUHEDVHGRQWKHIDFWWKDWPRQH\HDUQVLQWHUHVWRYHU WLPH7KHUHDUHWZRW\SHVRILQWHUHVWVLPSOHLQWHUHVWDQGFRPSRXQG LQWHUHVW7KHEDVLVIRU7LPH9DOXHRI0RQH\DQGFDVKIORZFDOFXODWLRQVLV FRPSRXQGLQWHUHVW Simple Interest ,QVLPSOHLQWHUHVWFRQWUDFWVLQWHUHVWLVDSHUFHQWRIWKHRULJLQDOSULQFLSDO 7KHLQWHUHVWDQGSULQFLSDODUHGXHDWWKHHQGRIWKHFRQWUDFW)RU H[DPSOHVD\\RXORDQWRDIULHQGIRUD\HDUDQG\RXZDQWWREH UHSDLGZLWK\bVLPSOHLQWHUHVW$WWKHHQGRIWKH\HDU\RXUIULHQGRZHV \RXLV\bRI\f6LPSOHLQWHUHVWFDOFXODWLRQVDUHGRQH XVLQJWKH D NH\RQ\RXU+3%,,$QH[DPSOHRIDVLPSOHLQWHUHVW FDOFXODWLRQLVRQSDJH .book Page 47 Wednesday, June 21, 2000 5:19 PM
48 4: Picturing Financial Problems Compound Interest $FRPSRXQGLQWHUHVWFRQWUDFWLVOLNHDVHULHVRIVLPSOHLQWHUHVWFRQWUDFWV WKDWDUHFRQQHFWHG7KHOHQJWKRIHDFKVLPSOHLQWHUHVWFRQWUDFWLVHTXDOWR RQHFRPSRXQGLQJSHULRG$WWKHHQGRIHDFKSHULRGWKHLQWHUHVWHDUQHG RQHDFKVLPSOHLQWHUHVWFRQWUDFWLVDGGHGWRWKHSULQFLSDO)RUH[DPSOHLI \RXGHSRVLWLQDVDYLQJVDFFRXQWWKDWSD\V\bDQQXDOLQWHUHVW FRPSRXQGHGPRQWKO\\RXUHDUQLQJVIRUWKHILUVWPRQWKORRNOLNHD VLPSOHLQWHUHVWFRQWUDFWZULWWHQIRUPRQWKDWó\b\b¸\f$WWKH HQGRIWKHILUVWPRQWKWKHEDODQFHRIWKHDFFRXQWLVLVó\b RI\f 7KHVHFRQGPRQWKWKHVDPHSURFHVVWDNHVSODFHRQWKHQHZEDODQFHRI 7KHDPRXQWRILQWHUHVWSDLGDWWKHHQGRIWKHVHFRQGPRQWKLV ó\bRIRU7KHFRPSRXQGLQJSURFHVVFRQWLQXHVIRUWKH WKLUGIRXUWKDQGILIWKPRQWKV7KHLQWHUPHGLDWHUHVXOWVLQWKLV LOOXVWUDWLRQDUHURXQGHGWRGROODUVDQGFHQWV 7KHZRUGFRPSRXQGLQFRPSRXQGLQWHUHVWFRPHVIURPWKHLGHDWKDW LQWHUHVWSUHYLRXVO\HDUQHGRURZHGLVDGGHGWRWKHSULQFLSDO7KXVLWFDQ HDUQPRUHLQWHUHVW7KHILQDQFLDOFDOFXODWLRQFDSDELOLWLHVRIWKH+3%,, DUHEDVHGRQFRPSRXQGLQWHUHVW 1 -1,000.00 1,005.00 2 -1,005.00 1,010.03 3 -1,010.03 1,015.08 4 -1,015.08 1,020.16 5 -1,020.16 1,025.26 10B.book Page 48 Wednesday, June 21, 2000 5:19 PM
4: Picturing Financial Problems 49 Interest Rates :KHQ\RXDSSURDFKDILQDQFLDOSUREOHPLWLVLPSRUWDQWWRUHFRJQL]HWKDW WKHLQWHUHVWUDWHRUUDWHRIUHWXUQFDQEHGHVFULEHGLQDWOHDVWWKUHH GLIIHUHQWZD\V n$VDSHULRGLFUDWH7KLVLVWKHUDWHWKDWLVDSSOLHGWR\RXUPRQH\IURP SHULRGWRSHULRG n$VDQDQQXDOQRPLQDOUDWH7KLVLVWKHSHULRGLFUDWHPXOWLSOLHGE\WKH QXPEHURISHULRGVLQD\HDU n$VDQDQQXDOHIIHFWLYHUDWH7KLVLVDQDQQXDOUDWHWKDWFRQVLGHUV FRPSRXQGLQJ ,QWKHSUHYLRXVH[DPSOHRIDVDYLQJVDFFRXQWWKHSHULRGLFUDWH LVó\bSHUPRQWK\fTXRWHGDVDQDQQXDOQRPLQDOUDWHRI\bóï\f 7KLVVDPHSHULRGLFUDWHFRXOGEHTXRWHGDVDQDQQXDOHIIHFWLYHUDWHZKLFK FRQVLGHUVFRPSRXQGLQJ7KHEDODQFHDIWHUPRQWKVRIFRPSRXQGLQJLV ZKLFKPHDQVWKHDQQXDOHIIHFWLYHLQWHUHVWUDWHLV\b ([DPSOHVRIFRQYHUWLQJEHWZHHQQRPLQDODQGDQQXDOHIIHFWLYHUDWHVDUH RQSDJHVWKURXJK Two Types of Financial Problems 7KHILQDQFLDOSUREOHPVLQWKLVPDQXDOXVHFRPSRXQGLQWHUHVWXQOHVV VSHFLILFDOO\VWDWHGDVVLPSOHLQWHUHVWFDOFXODWLRQV)LQDQFLDOSUREOHPVDUH GLYLGHGLQWRWZRJURXSV790SUREOHPVDQGFDVKIORZSUREOHPV Recognizing a TVM Problem ,IXQLIRUPFDVKIORZVRFFXUEHWZHHQWKHILUVWDQGODVWSHULRGVRQWKH FDVKIORZGLDJUDPWKHILQDQFLDOSUREOHPLVD790WLPHYDOXHRIPRQH\\f SUREOHP7KHUHDUHILYHPDLQNH\VXVHGWRVROYHD790SUREOHP P1XPEHURISHULRGVRUSD\PHQWV .$QQXDOSHUFHQWDJHLQWHUHVWUDWHXVXDOO\WKHDQQXDOQRPLQDOUDWH\f 3UHVHQWYDOXHWKHFDVKIORZDWWKHEHJLQQLQJRIWKHWLPHOLQH\f 23HULRGLFSD\PHQW /)XWXUHYDOXHWKHFDVKIORZDWWKHHQGRIWKHFDVKIORZGLDJUDP LQDGGLWLRQWRDQ\UHJXODUSHULRGLFSD\PHQW\f 10B.book Page 49 Wednesday, June 21, 2000 5:19 PM