FOMGT 301. Spring 2004

Transcription

1 MMQ Problems d Set of Solutios FOMGT 301 Sprig Adrew Hall. MMQ Solutios Two. Page 1

2 MMQ 11: Remember Newma? He spis the wheel, ad receives $10,000 immediately. Alteratively, he ca leave it with the machie for years to ear iterest of 10% compouded semi-aually. How much will he have? Kow Ukow $10,000??? r 10% 0.10 m We use formula 3.3 m 1 + { rm} 1+ { } 4 [ ] 5 * Compoudig semi-aually at 10% per aum over two years is the same thig as compoudig periodically at 10% / (where is the # of compoudig periods i a year) or 5% per period over 4 periods: So we could use formula 3. but with r 5% ad * ( 1+ r) 4 ( ) ( ) * , All that is left is to crak the calculatio through the calculator APPS TI83-Plus TI-83 HP10B TI-BAII Plus Sharp {Set Decimals to d DISP 6 d FORMAT 6} [See News [Sets the 6 ENTER Page Chapter places of 14.] decimals d QUIT displayed to 6] ENTER d FINANCE d CLEAR ALL [Clears all of the stored variables] d CLEAR TVM {Set Decimals to 6} [I have t got a Sharp, so look i the maual.} {Clear all variables} [look i the maual.] 004 Adrew Hall. MMQ Solutios Two. Page

3 [ 10,000 Store As ] [ Store As N ] 10 I/YR [ 10 Store As I/YR ] 10 I/Y 10 i Poit to get cursor i 0 Lie Poit to get cursor i 0 Lie d xp/yr [ Store As xp/yr ] to get {Set Coupos Per Period to } [see below] CPT to get {Set Coupos Per Period to } [look i the maual.] COMP to get Settig Coupos per period with the TI-BAII Plus. d P/Y takes you ito a subroutie. The up ad dow keys toggle betwee settig P/Y ad settig C/Y. C/Y is coupos per period or the umber of times iterest is compouded i the period for which the iterest rate is give. Toggle to C/Y eter the value you wat (i our problem mc/y). Hit the ENTER key. Leave the sub-routie by d QUIT MMQ 1: Retur to MMQ 11. Same problem, except that 10% iterest compouds daily. How much will he have? Kow Ukow $10,000??? r 10% 0.10 M365 (days i a regular year) 004 Adrew Hall. MMQ Solutios Two. Page 3

4 We use formula m 1 + { rm} 365* 1 + { } [ ] * , All that is left is to crak the calculatio through the calculator APPS TI83-Plus TI-83 HP10B TI-BAII Plus Sharp {Set Decimals to d DISP 6 d FORMAT 6} [See News [Sets the 6 ENTER Page Chapter places of 14.] decimals d QUIT displayed to 6] ENTER d FINANCE d CLEAR ALL [Clears all of the stored variables] d CLEAR TVM {Set Decimals to 6} [I have t got a Sharp, so look i the maual.} {Clear all variables} [look i the maual.] [ 10,000 Store As ] 365 d P/YR [ 365 Store As P/YR ] d xp/yr [ * P/YR Store As N ] 10 I/YR [ 10 Store As I/YR ] 10 I/Y {Set Coupos Per Period to 365} [see above] 10 i {Set Coupos Per Period to 365} [look i the maual.] Poit to get cursor i 0 Lie Poit to get cursor i 0 Lie to get CPT to get COMP to get 004 Adrew Hall. MMQ Solutios Two. Page 4

5 MMQ 13: Retur to MMQ 11. Same problem, except that 10% iterest compouds cotiuously. How much will he have? Kow Ukow $10,000??? r 10% 0.10 m (ifiity) Actually there is aother formula Cotiuous Compoudig: * r e (3.4) Calculator Check! Do you have the e key? If yes, the lear how to use it. If ot, the you ll eed to thik of Formula (3.4) as: {.7188 r } So all we eed to do is crak the umbers: Usig e ad the formula o a TI-Calculator e 10000* r* 0.10* * * [ ] 0. 1, , Adrew Hall. MMQ Solutios Two. Page 5

6 All that is left is to crak the calculatio through the calculator APPS TI83-Plus TI-83 HP10B TI-BAII Plus Sharp {Set Decimals to d DISP 6 d FORMAT 6} [See News [Sets the 6 ENTER Page Chapter places of 14.] decimals d QUIT displayed to 6] ENTER d FINANCE d CLEAR ALL [Clears all of the stored variables] d CLEAR TVM {Set Decimals to 6} [I have t got a Sharp, so look i the maual.} {Clear all variables} [look i the maual.] [ 10,000 Store As ] Poit to get cursor i 0 Lie Poit to get cursor i 0 Lie d P/YR [ Store As P/YR ] d xp/yr [ * P/YR Store As N ] 10 I/YR [ 10 Store As I/YR ] to get 10 I/Y {Set Coupos Per Period to } [see above MMQ1] CPT to get 10 i COMP to get 004 Adrew Hall. MMQ Solutios Two. Page 6

7 MMQ 14: Let s go back to MMQ 1, where we leared that $8.64 is equivalet to receivig $100 i two years at a particular iterest rate. Solve for that rate. Kow Ukow $8.64 r??? $ Solvig for the iterest rate: r 1 1 (3.10) So all we eed to do is crak the umbers: Usig the formula o a TI-Calculator r r r r 0.10 or 10 percet All that is left is to crak the calculatio through the calculator APPS TI83-Plus TI-83 HP10B TI-BAII Plus Sharp {Set Decimals to d DISP 6 d FORMAT 6} [See News [Sets the 6 ENTER Page Chapter places of 14.] decimals d QUIT displayed to 6] {Set Decimals to 6} [I have t got a Sharp, so look i the maual.} 004 Adrew Hall. MMQ Solutios Two. Page 7

8 ENTER d FINANCE d CLEAR ALL [Clears all of the stored variables] d CLEAR TVM {Clear all variables} [look i the maual.] 8.64 [ 8.64 Store As ] [ Store As ] [ Store As N ] Poit to get cursor i I%0 Lie Poit to get cursor i I%0 Lie I/YR to get CPT I/Y to get COMP i to get MMQ 15: The wheel lads o $100,000 to be received immediately. But what Newma really wats i life is to ope a Fat-Free Yogurt Store, ad he kows that to purchase such a store will take $165,000. If Newma takes the optio of leavig the moey with the Moey Machie, ad if the moey ears 10% aually, how log will he have to wait? Kow Ukow $100, r 0.10 or 10%??? $165, Rearrage formula (3.) ( 1+ r) to get (3.11) ( 1+ r) { } ad take the atural logarithm of both sides of the equatio to get: 004 Adrew Hall. MMQ Solutios Two. Page 8

9 *l ( 1+ r) l Divide both sides by l(1+r) to get l l ( 1+ r) So all we eed to do is crak the umbers: l l ( ) ( ) l 1.65 Usig the formula o a TI-Calculator l( 1.10) Ufortuately his dream will take over 5 years to realize. All that is left is to crak the calculatio through the calculator APPS TI83-Plus TI-83 HP10B TI-BAII Plus Sharp {Set Decimals to d DISP 6 d FORMAT 6} [See News [Sets the 6 ENTER Page Chapter places of 14.] decimals d QUIT displayed to 6] ENTER d FINANCE d CLEAR ALL [Clears all of the stored variables] d CLEAR TVM {Set Decimals to 6} [I have t got a Sharp, so look i the maual.} {Clear all variables} [look i the maual.] 004 Adrew Hall. MMQ Solutios Two. Page 9

10 [ 100,000 Store As ] [ 165,000 Store As ] I/YR [ 10 Store As I/YR ] 10 I/Y 10 i Poit to get cursor i N0 Lie Poit to get cursor i N0 Lie N to get CPT N to get COMP N to get 004 Adrew Hall. MMQ Solutios Two. Page 10