C H A P T E R 2 Classc Problems at a Glace usg the TVM Solver The table below llustrates the most commo types of classc face problems. The formulas are gve for each calculato. A bref troducto to usg the TVM Solver s followed by a example of each of the formulas the table. Future Value Preset Value Lump Sum Compoud Amout Factor ( 1+ ) Preset Value Factor 1 ( 1+ ) ( 1 ) = + - Auty Auty Compoud Amout Factor 1+ -1 Auty Preset Value Factor 1-1+ - Skg Fud Factor 1+ -1 Captal Recovery Factor or Loa Repaymet Factor 1-1+ - Calculator Housekeepg Detal Settg the Mode 1. Press the z key (2B) ad chage the Float to 2. Ths wll cause decmal aswers to dsplay wth 2 dgts sce most aswers face are dollars ad cets. Hghlght 2 o the secod le ad press Í to save your selecto. (Fgure 1) (Fgure 1) 2. Use y [QUIT] (2B) to retur to the Home Scree. Refer to the secto o Key Arragemet Chapter 1 for a explaato of the key locator codes used ths maual. 1997 TEXAS INSTRUMENTS INCORPORATED TIME, VALUE, MONEY: APPLICATIONS ON THE TI-83 5
Calculator Housekeepg Detal Usg the TVM Solver 1. Press y [FINANCE] (5A). Choose 1:TVM Solver from the CALC meu by pressg 1 or Í. (Fgure 2) (Fgure 2) The scree that appears wll be smlar to Fgure 3 but wll probably have dfferet values. Iterest s smple or compouded. I the TVM Solver, the umber of compoudg perods per year (C/Y) s set to 1 for smple terest; otherwse t dcates the umber of compoudg perods per year. For cotuous compoudg, set C/Y to a very large umber, e.g., 1 E 11. (See Chapter 6, Cotuous Compoudg for detals.) 2. Whe usg the TVM Solver, eter values for each of the varables: N Number of paymet perods I% Aual terest rate PV Preset Value PMT Paymet Amout FV Future Value P/Y Number of paymet perods per year C/Y Number of compoudg perods per year PMT: Idcates whether paymets are made at the ed or begg of each paymet perod. (Fgure 3) Note: Store C/Y after storg P/Y because a chage P/Y always resets C/Y. (Fgure 3) 3. Eter the umber of years for N, I% as a percet (ot as a decmal). Eter the moey vested as a egatve umber (cash outflows are cosdered egatve, whle cash flows are cosdered postve). Eter the paymet (PMT) as 0, ad the paymets per year (P/Y) as 1. 4. To solve, move the cursor to the varable for whch you wat to solve. Press ƒ [SOLVE] (10E) to calculate ths value. A small shaded box to the left of the varable dcates a soluto. If you chage a value o the scree, you wll lose the shaded box ad must solve aga for a ew value. Compoud Amout Factor ( 1+ ) Example 1: What ca a vestor expect to receve at the ed of a year f he deposts $200 a bak gvg 10% terest? 1. Press y [FINANCE] (5A) ad choose 1:TVM Solver from the CALC meu. (Fgure 4) 2. As step 3 above, eter N = 1, I% = 10, PV = -200, PMT = 0, P/Y = 1 ad C/Y = 1. Leave PMT: set to END. 3. Place the cursor o the Future Value (FV), the press ƒ [SOLVE] (10E). The future value s $220.00. (Fgure 4) 6 TIME, VALUE, MONEY: APPLICATIONS ON THE TI-83 1997 TEXAS INSTRUMENTS INCORPORATED
Example 2: How log wll t take a dollar to double at 8% compouded semaually? 1. Press y [FINANCE] ad choose 1:TVM Solver (Fgure 5) 2. I ths example, I% = 8, PV = -1, PMT = 0, FV = 2, P/Y = 2 ad C/Y = 2. To eter these values, put 8 Ì 1 0 2 2 2. 3. Place the cursor o the N ad the press ƒ [SOLVE] (10E) to fd the umber of perods. (Fgure 5) It takes 17.67 paymet perods, or 17.67 half-years. That s about 9 years. (Fgure 6) 4. By chagg P/Y to 1, we ca fd the aswer years. Set P/Y = 1 ad C/Y = 2. (Fgure 6) 5. Move the cursor to the frst le, N= ad press ƒ [SOLVE] (10E). (Fgure 7) Note: N = 8.84 years sce the umber of paymets per year s set to 1. (Fgure 7) 1 1+ Preset Value Factor ( 1 ) = + - Example 3: What amout eeds to be deposted a vestmet that yelds 5% so that t wll be worth $600 at year ed? (Fgure 8) 1. Iput 1 for N because the umber of paymet perods s oe, 5 for the terest rate (I%), 0 as the paymet (PMT), 600 as the future value (FV), ad 1 for both paymets per year (P/Y), ad compoudgs per year (C/Y). 2. Place the cursor o PV ad press ƒ [SOLVE] (10E) to fd the preset value. (Fgure 8) Oe eeds to depost $571.43 a vestmet that yelds 5% so that t wll be worth $600 at year ed. 1 + - 1 Auty Compoud Amout Factor Example 4: What ca a face teacher wthdraw from her accout f she saves $1,000 a year for 3 years at 5% terest? (Fgure 9) 1. Iput 3 for N because there are 3 paymet perods, 5 for the terest rate (I%), 0 as the preset value (PV), -1000 for the paymet (PMT), 1 for paymets per year (P/Y), ad 1 for compoudg per year (C/Y). Note that PMT s egatve because the teacher s payg out $1,000 every year. 2. Place the cursor o FV ad press ƒ [SOLVE] (10E) to fd the future value. (Fgure 9) I three years, the face teacher ca wthdraw $3,152.50. 1997 TEXAS INSTRUMENTS INCORPORATED TIME, VALUE, MONEY: APPLICATIONS ON THE TI-83 7
Example 5: A bologst deposts $1,000 her accout at the ed of each quarter for 10 years. How much moey does she have at the ed of 10 years f the bak pays 6% terest compouded quarterly? The umber of paymet perods s 40 because she s makg deposts four tmes a year for 10 years. Eter 0 for the preset value (PV). The PMT must be etered as a egatve umber because t represets a outflow from the pocket of the bologst. The paymets per year (P/Y) ad the compoudg per year (C/Y) are both 4 for quarterly compoudg. The paymets are at the ed of each quarter, so hghlght END rather tha BEGIN the last le of the TVM Solver. (Fgure 10) 1. Iput the formato, the move the cursor to FV ad press ƒ [SOLVE] (Fgure 10) (Fgure 11) (10E) to fd the preset value. (Fgure 11) At the ed of 10 years, the bologst has $54,267.89. Example 6: The bologst the last exercse decded that she wated to have $54,267.89 her accout 10 years ad she foud a bak whch compouded mothly at 6%. What are her mothly paymets to acheve her goal of $54,267.89? 1. Chage the umber of paymets (N) to 120 because the paymets are ow mothly for 10 years, ad chage the P/Y ad C/Y to 12 because both ow occur mothly. (Fgure 12) 2. Place the cursor o the paymet (PMT) ad press ƒ [SOLVE] (10E) to fd the amout of the paymets. (Fgure 12) The bologst must make mothly paymets of $331.15 to acheve her goal of $54,267.89. Notce that 120 paymets at $331.15 amouts to $39,738 out of the pocket versus 40 paymets of $1,000 each whch amouts to $40,000. Auty Preset Value Factor 1-1+ - Example 7: What would gradparets have to sped to establsh a payout of $2,000 per year for 3 years to ther gradso at 5% terest? (Fgure 13) 1. Let the umber of paymets (N) be 3 because the payout s aual for 3 years. The terest rate (I%) s 5, the paymet (PMT) of 2000 s postve because t s comg to the gradso. Eter 0 for the future value (FV), 1 for paymets per year (P/Y) ad 1 for compoudg per year (C/Y). 2. Place the cursor o the preset value (PV) ad press ƒ [SOLVE] (10E) to fd the preset value. (Fgure 13) The gradparets should vest $5,446.50. The preset value s egatve o the calculator scree because that s the amout that the gradparets must pay out to establsh the gradso s auty. 8 TIME, VALUE, MONEY: APPLICATIONS ON THE TI-83 1997 TEXAS INSTRUMENTS INCORPORATED
Skg Fud Factor ( 1+ ) -1 Example 8: At the ed of 3 years, a busess perso eeds to have $4,000 avalable to buy a ew computer. How much moey must he depost each year at 5% terest? (Fgure 14) 1. Iput 3 for the umber of paymets (N), 5 for the terest rate (I%), 0 for the preset value (PV), 4000 as a postve value for the future value (FV), 1 for the paymets per year (P/Y), ad 1 for the compoudg per year (C/Y). 2. Place the cursor o the paymet (PMT) ad press ƒ [SOLVE] (10E) to fd the aual paymet. (Fgure 14) The aual paymet s $1,268.83. The aual paymet s egatve o the calulator scree because t represets the amout that the busess perso must pay out every year. Captal Recovery Factor or Loa Repaymet Factor 1- ( 1+ ) - Example 9: What mothly paymet would a college seor make to pay off a used car loa of $2,000 at 12% by the ed of the year? (Fgure 15) 1. Because there are mothly paymets for a year, eter 12 for the umber of paymets (N), eter 12 for the terest rate (I%), 2000 for the preset value (PV), 0 for the future value (FV), 12 for the paymets per year (P/Y), ad 12 for the compoudg per year (C/Y). Note that (PV) s etered as a postve 2000 because the studet has the moey had. 2. Place the cursor o the paymet (PMT) ad press ƒ [SOLVE] (10E) to fd the mothly paymet. (Fgure 15) The mothly paymet wll be $177.70. The mothly paymet s egatve o the calculator scree because the amout represets the amout that the college seor must pay out every moth. 1997 TEXAS INSTRUMENTS INCORPORATED TIME, VALUE, MONEY: APPLICATIONS ON THE TI-83 9